a basketball player is running at 4.45 m/s toward the basket when he jumps into the air to dunk the ball. he maintains the same horizontal velocity while in the air.

Answer:

a) 500 N

b) 250 J

c) 0.87 m

d) 1.58 m/s, at 0.6 m from the wall

Explanation:

The mass of the object m = 100 kg

the spring constant k = 1000 N/m

length of the the spring = 1 m

extension of the string = 50 cm = 0.5 m

a) Force used to pull the mass is gotten from Hooke's law equation

F = -kx

where F is the force used to pull = ?

k is the spring constant = 1000 N/m

x is the extension = 0.5 m

substituting, we have

F = 1000 x 0.5 = 500 N  this force is used to pull the mass

b) The work done in moving the mass = Fx

==> 500 x 0.5 = 250 J

c) The energy stored up in the spring U = \(\frac{1}{2}kx^{2}\)

U = \(\frac{1}{2}*1000*0.5^{2}\) = 125 J

energy available for the mass from its equilibrium position = 250 - 125 = 125 J

this energy is equivalent to the work done by the spring on the mass by moving it closer to the wall

Work W = (weigh of the mass) x distance moved

weight = mg

where m is the mass = 100 kg

g is acceleration due to gravity = 9.81 m/s^2

substituting, we have

W = mgd

where d is the distance the mass moves closer to the wall

W = 100 x 9.81 x d

but W = 125 J

125 = 981d

d = 125/981 = 0.13 m

closeness to the wall = L - d

where L is the natural length of the spring = 1 m

closeness to the wall = 1 - 0.13 = 0.87 m

d) The maximum kinetic energy of the object  will be halfway between the extended length and the final resting place.

extended length = 1 + 0.5 m = 1.5 m

distance from resting place = 1.5 - 0.87 = 0.63 m from the wall

At this point, all the mechanical energy on the mass and spring system is converted to kinetic energy of motion.

KE = \(\frac{1}{2}mv^{2}\)

substituting,

125 = \(\frac{1}{2}*100*v^{2}\) = \(50v^{2}\)

\(v^{2}\) = 125/50 = 2.5

v = \(\sqrt{2.5}\) = 1.58 m/s

Answer:nh

0.750 kg hammer is moving horizontally at 7.00 m/s when it strikes a nail and comes to rest after driving it 1.00 cm into a board.

The amount of energy lost to friction, sound, and other factors during the collision is 48620.15 J.

In the event of a car collision, the momentum of the two vehicles changes as a result of the impact, and energy is transferred from one vehicle to the other.

The impact will result in a loss of energy due to friction, sound, and other factors. Therefore, to calculate the amount of energy lost during the collision, we need to determine the total kinetic energy of the system before and after the collision, and the difference between the two is the energy lost.

To calculate the initial kinetic energy, we need to use the formula 1/2mv², where m is the mass of the object and v is its velocity. Therefore, the initial kinetic energy of car 1 is:KE1 = 1/2 x 1300 kg x (12.5 m/s)² = 101562.5 J The stationary car has no initial kinetic energy since it is at rest.

The total initial kinetic energy of the system is therefore: KE initial = KE1 + KE2 = 101562.5 J To calculate the final kinetic energy, we need to use the velocity of the two cars after the collision.

The problem states that the two cars slide off with a velocity of 6.3 m/s. Therefore, the final kinetic energy of the system is: KE final = 1/2 x (1300 kg + 1500 kg) x (6.3 m/s)² = 52942.35 J.

The energy lost during the collision is the difference between the initial and final kinetic energy: Energy lost = KE initial - KE final = 48620.15 J.

Therefore, the amount of energy lost to friction, sound, and other factors during the collision is 48620.15 J.

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T sin θ = M g = W     cable supporting weight

T = 100 * 9.8 / sin 40 = 1525 N

T cos θ = Th horizontal force due to cable

Th = 1525 cos 40 = 1168 N

Answer:

Since velocity is considered a vector quantity and vectors show you in what direction it goes the object wont be moving forward but backwards because its a negative and negatives go to the left and that would be considered backwards.

Explanation:

Hope this helps

Answer:

True

Explanation:

the independent variable would be like if the psychologist is experimenting the impact of sleep deprivation, sleep deprivation would be the independent variable that is being manipulated or changing its level systematically in the experiment.

D. lost an electron

because they have free electron in the outermost shell which they will like to denote, in order to attain stable configuration

Answer:

44°

Explanation:

Look for the longest distance under the 'Distance ' column....look to the left to find the corresponding angle

  Table clearly shows that the longest distance (133 ft) occurs at angle of 44°

Answer:  lose weight at high altitudes.

Explanation:

Answer:

Just a week at high altitudes can cause sustained weight loss, suggesting that a mountain retreat could be a viable strategy for slimming down. Overweight, sedentary people who spent a week at an elevation of 8,700 feet lost weight while eating as much as they wanted and doing no exercise

The velocity of the roller coaster at location 4 is 14.14 m/s (approx) using the given values of v₁ = 10 m/s, h₁ = 30 m, and h₂ = 15 m.

Roller coasters are fascinating machines that deliver an exhilarating experience by defying gravity and physics. Roller coaster physics is a significant concept to comprehend before riding a roller coaster or designing one. The laws of physics govern the motion of a roller coaster, including its velocity, acceleration, and potential energy.

A roller coaster moves over a crest at location 1 with a speed of 10 m/s. The question is how fast it's going at location 4, considering the neglect of friction and air resistance. To solve this, we'll need to consider the conservation of energy law.

The total energy of the roller coaster remains constant throughout the ride, and we can convert between potential and kinetic energy.Using the conservation of energy formula, which is: E1 = E2Where E1 is the total energy of the roller coaster at the crest and E2 is the total energy of the roller coaster at location 4.

Both E1 and E2 comprise kinetic energy (KE) and potential energy (PE). So,E1 = KE1 + PE1E2 = KE2 + PE2Since the roller coaster has no friction and air resistance, we can assume that PE1 = PE2 because the height of the roller coaster doesn't change. The energy is converted from potential energy at the crest to kinetic energy at location 4.

We can now use the formula for kinetic energy:KE = (1/2) mv²Where m is the mass of the roller coaster and v is its velocity. Both E1 and E2 can be written in terms of KE, so: E1 = (1/2) mv₁²E2 = (1/2) mv₂².

Substitute the values into the conservation of energy formula: E1 = E2(1/2) mv₁² = (1/2) mv₂²

Simplifying the equation gives:v₂² = v₁²×(h₁ / h₂)

where h₁ is the height of the crest and h₂ is the height of location 4.

To calculate the velocity, we need to take the square root of both sides:v₂ = v₁×√(h₁ / h₂)

Therefore, the velocity of the roller coaster at location 4 is 14.14 m/s (approx) using the given values of v₁ = 10 m/s, h₁ = 30 m, and h₂ = 15 m.

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The velocity of the third piece is v₃ = -12500 kg·m/s / m₃

The law of conservation of momentum states that the total momentum before the explosion is equal to the total momentum after the explosion.

velocity of the third piece =  v₃.

The total initial momentum before the explosion = 0

The total final momentum after the explosion= 0

Initial momentum = 0 kg·m/s (since the bomb is at rest)

Final momentum = m₁v₁ + m₂v₂ + m₃v₃

m₁ = mass of the first piece = 150 kg

v₁ = velocity of the first piece = 150 m/s (to the east)

m₂ = mass of the second piece = 100 kg

v₂ = velocity of the second piece = 200 m/s (south 60° west)

m₃ = mass of the third piece = unknown

v₃ = velocity of the third piece = unknown

0 = (150 kg)(150 m/s) + (100 kg)(200 m/s)(cos(60°)) + (m₃)(v₃)

final momentum = 0 and hence  v₃ is found as :

0 = 22500 kg·m/s - 10000 kg·m/s + (m₃)(v₃)

-12500 kg·m/s = (m₃)(v₃)

v₃ = -12500 kg·m/s / m₃

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I apologize, but I can't help with the specific calculations you've provided. Calculating forces and friction coefficients requires specific numerical values and equations. However, I can explain the concepts and provide a general understanding of the questions you've asked.

3.1 To calculate the magnitude of the force exerted by the athlete vertically on the track, you need the vertical component of the force applied. If the angle of 50° is measured from the horizontal, you can calculate the vertical component using the equation: horizontal force = force × sin(angle).

3.2 To calculate the magnitude of the force exerted by the athlete horizontally on the track, you need the horizontal component of the force applied. Using the same angle of 50° measured from the horizontal, you can calculate the horizontal component using the equation: vertical force = force × cos(angle).

3.4 To determine the minimum value of the static friction coefficient, you would need additional information such as the mass of the athlete. In addition, you would need the normal track force. The coefficient of static friction is a dimensionless value that represents the maximum frictional force that can exist between two surfaces without causing them to slip. The formula to calculate static frictional force is static frictional force = coefficient of static friction × normal force.

3.5 To determine the resultant force exerted on an object when three forces are applied, you need to calculate the vector sum of the forces. You can add forces vectorially by breaking them down into their horizontal and vertical components. You can also sum up the components separately, and then combine them to find the resultant force.

Please provide more specific numerical values or equations if you would like assistance with the calculations.

Answer:

a) The x-position of the skateboarder is 0.324 meters.

b) The y-position of the skateboarder is -2.16 meters.

c) The x-velocity of the skateboard is 1.08 meters per second.

d) The y-velocity of the skateboard is -3.6 meters per second.

Explanation:

a) The x-position of the skateboarder is determined by the following expression:

\(x(t) = x_{o} + v_{o,x}\cdot t + \frac{1}{2}\cdot a_{x} \cdot t^{2}\) (1)

Where:

\(x_{o}\) - Initial x-position, in meters.

\(v_{o,x}\) - Initial x-velocity, in meters per second.

\(t\) - Time, in seconds.

\(a_{x}\) - x-acceleration, in meters per second.

If we know that \(x_{o} = 0\,m\), \(v_{o,x} = 0\,\frac{m}{s}\), \(t = 0.60\,s\) and \(a_{x} = 1.8\,\frac{m}{s^{2}}\), then the x-position of the skateboarder is:

\(x(t) = 0\,m + \left(0\,\frac{m}{s} \right)\cdot (0.60\,s) + \frac{1}{2}\cdot \left(1.8\,\frac{m}{s^{2}} \right) \cdot (0.60\,s)^{2}\)

\(x(t) = 0.324\,m\)

The x-position of the skateboarder is 0.324 meters.

b) The y-position of the skateboarder is determined by the following expression:

\(y(t) = y_{o} + v_{o,y}\cdot t + \frac{1}{2}\cdot a_{y} \cdot t^{2}\) (2)

Where:

\(y_{o}\) - Initial y-position, in meters.

\(v_{o,y}\) - Initial y-velocity, in meters per second.

\(t\) - Time, in seconds.

\(a_{y}\) - y-acceleration, in meters per second.

If we know that \(y_{o} = 0\,m\), \(v_{o,y} = -3.6\,\frac{m}{s}\), \(t = 0.60\,s\) and \(a_{y} = 0\,\frac{m}{s^{2}}\), then the x-position of the skateboarder is:

\(y(t) = 0\,m + \left(-3.6\,\frac{m}{s} \right)\cdot (0.60\,s) + \frac{1}{2}\cdot \left(0\,\frac{m}{s^{2}}\right)\cdot (0.60\,s)^{2}\)

\(y(t) = -2.16\,m\)

The y-position of the skateboarder is -2.16 meters.

c) The x-velocity of the skateboarder (\(v_{x}\)), in meters per second, is calculated by this kinematic formula:

\(v_{x}(t) = v_{o,x} + a_{x}\cdot t\) (3)

If we know that \(v_{o,x} = 0\,\frac{m}{s}\), \(t = 0.60\,s\) and \(a_{x} = 1.8\,\frac{m}{s^{2}}\), then the x-velocity of the skateboarder is:

\(v_{x}(t) = \left(0\,\frac{m}{s} \right) + \left(1.8\,\frac{m}{s} \right)\cdot (0.60\,s)\)

\(v_{x}(t) = 1.08\,\frac{m}{s}\)

The x-velocity of the skateboard is 1.08 meters per second.

d) As the skateboarder has a constant y-velocity, then we have the following answer:

\(v_{y} = -3.6\,\frac{m}{s}\)

The y-velocity of the skateboard is -3.6 meters per second.

Answer: D

Explanation: it seem right to me I really don't know if this right but I hope this helps

5789.8 W  is the average power of the elevator motor during this period and 1.115 * 10⁴ W this power compare with the motor power when the elevator moves at its cruising speed.

The rate with which the speed and direction of a moving object vary over time. A point a object going straight ahead is pushed when it accelerates or decelerates.

Mass of elevator = 650 kg

Time = 4.50 sec

Speed of the elevator = 1.75 m/s

Calculating the elevator's acceleration is necessary.

Using the acceleration formula

a = vf - vi / t

a = 1.75 / 4.50

a = 0.38 m/s2

(a). We must determine the net force acting on the elevator.

Using the force formula

T = mg + ma

T = m (g +a)

T = 650 (9.8 + 0.38)

T = 6617 N

We must determine the average velocity.

Using the average velocity formula

v' = vf + vi / 2

v' = 1.75 / 2

v' = 0.875 m/s

We must determine the average power.

Using the power formula

P = T * v'

P = 6617 * 0.875

P = 5789.8 W

(b). We must determine the motor's power input.

Using the power formula

P = F * v

P = mg * v

P = 650 * 9.8 * 1.75

P = 1.115 * 10⁴ W.

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Answer:

Molecule would be correct.

Explanation:

Answer:

The value is  \(B = 0.0643 \ T\)  

Explanation:

From the question we are told that

   The length of the solenoid is  \(L = 133 \ cm = 1.33 \ m\)

     The radius is  \(r = 2.99 \ cm = 0.0299 \ m\)

     The number of turns is \(N = 1740 \ turns\)

     The current it carries is  \(I = 3.91 \ A\)

Generally the magnitude of the magnetic field is mathematically represented as

           \(B = \frac{\mu_o * N * I}{L}\)

Here  \(\mu_o\)  is the permeability of free space with value  \(\mu_o = 4\pi *10^{-7} \ N/A^2\)

=>      \(B = \frac{ 4\pi * 10^{-7} * 1740 * 3.91}{0.133}\)  

=>      \(B = 0.0643 \ T\)  

Answer:

85

Explanation:

soln

given that;

frequency=17Hz

wavelength=5m

speed?

formula for wavelength is;

wavelength= speed/frequency

then ; making v the subject formula

we have that v=wavelength*frequency

v=17*5=>85ms

The potential energy of the roller coaster is 176,400 J (joules).

The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.

In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).

Using the formula, we can calculate the potential energy:

PE = mgh

= (900 kg)(9.8 \(m/s^2\))(20 m)

= 176,400 J

Therefore, the potential energy of the roller coaster is 176,400 J (joules).

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A 66.1-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. He then drops through a height of 1.59 m, and ends with a speed of 8.51 m/s. The nonconservative work done on the boy is approximately -42.7 kilojoules.

To find the nonconservative work done on the boy, we need to consider the change in the boy's mechanical energy during the process. Mechanical energy is the sum of the boy's kinetic energy (KE) and gravitational potential energy (PE).

The initial mechanical energy of the boy is given by the sum of his kinetic energy and potential energy when he catches the wave:

E_initial = KE_initial + PE_initial

The final mechanical energy of the boy is given by the sum of his kinetic energy and potential energy after he drops through the height:

E_final = KE_final + PE_final

The nonconservative work done on the boy is equal to the change in mechanical energy:

Work_nonconservative = E_final - E_initial

Let's calculate each term:

KE_initial = (1/2) * m * v_initial^2

= (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = m * g * h_initial

= 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * m * v_final^2

= (1/2) * 66.1 kg * (8.51 m/s)^2

PE_final = m * g * h_final

= 66.1 kg * 9.8 m/s^2 * 0

Since the boy ends at ground level, the final potential energy is zero.

Substituting the values into the equation for nonconservative work:

Work_nonconservative = (KE_final + PE_final) - (KE_initial + PE_initial)

Simplifying:

Work_nonconservative = KE_final - KE_initial - PE_initial

Calculating the values:

KE_initial = (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * 66.1 kg * (8.51 m/s)^2

Substituting the values:

Work_nonconservative = [(1/2) * 66.1 kg * (8.51 m/s)^2] - [(1/2) * 66.1 kg * (1.60 m/s)^2 - 66.1 kg * 9.8 m/s^2 * 1.59 m]

Calculating the result:

Work_nonconservative ≈ -42.7 kJ

Therefore, the nonconservative work done on the boy is approximately -42.7 kilojoules. The negative sign indicates that work is done on the boy, meaning that energy is transferred away from the boy during the process.

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Answer:3000

Explanation:

given:u=0v=20m/st= 8sec

thereforea=v-u/t=20-0/8=20/8=5/2 m/som=1200 kg

thereforef=ma=1200*5/2=600*5=3000N

Answer:

i say it would be 32.5 m if the brakes comes and stops.  the road is 3.7 x 105

Explanation:

Explanation:

m = 4kg

u = 20m/s

t = 10s

v = 60m/s

initial momentum = mass × initial velocity

= 4 × 20 = 80kgm/s

(a) The maximum acceleration the car can have without causing the cup to slide is 1.96 m/s².

(b) The smallest amount of time in which the person can accelerate the car from rest to the final speed is 12.25 seconds.

The maximum acceleration the car can have without causing the cup to slide is calculated as follows;

For the car not to slide, the applied force must equal the force of friction, so the that the acceleration of the car is zero.

F - Ff = ma

F - Ff = 0

F = Ff

ma = μmg

a = μg

where;

a = 0.2 x 9.8 m/s²

a = 1.96 m/s²

The smallest amount of time in which the person can accelerate the car from rest to the final speed is calculated as follows;

v = u + at

v = 0 + at

t = v/a

t = (24 m/s) / (1.96)

t = 12.25 s

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Answer:

\(375\:\mathrm{N}\)

Explanation:

Work is given by the equation \(W=F\Delta x\). Plugging in given values, we get:

\(W=75\cdot 5=\fbox{$ 375\:\mathrm{N}$}\).

Answer:

Note: 1 watt * 1000 hrs = 1 kWh    

         1 watts * 10,000 hrs = 10 kWh

Incandescent for 1000 hrs

Original cost = .51

  Usage = 122 W * .06  = 7.32

Total cost for 1000 hrs 7.32 + .51 = 7.83

Total cost for 10,000 = 78.3

CFL Bulb for 10,000 hrs

Original cost = 5.88

 Usage = 18  * .06 / kWh * 10 kWh = 10.8

Total cost = 5.88 + 10.8 = 16.68

Gives a total savings of 78.3 - 16.68 = 61.62

Another way of looking at this:

Note: the cost of electricity for the incandescent bulb is:

122 W * 1000 hr * .06 / kWh = 122 kWh * 06 = 7.32  for each KWh

That is 73.2 for 10 kWh   and 5.1 for bulb cost = 78.3

The CFL bulb uses in 10,000 hrs

18 kWh * 10 * .06 = 10.8    cost of electricity

bulb cost = 5.88  for a total cost of 16.68

If the purchase price of an incandescent bulb is $0.51 and for the CFL it is $5.88. The cost of electricity is 0.06 $ per kWh, then her total savings over the lifetime of the CFL would be 61.62 $.

The rate of doing work is known as power. The Si unit of power is the watt.

Power = work/time

As given in the problem to save energy and money, Jackie Smith replaced the 122 Watt incandescent light bulb in her house with an 18 Watt CFL bulb. The expected life of incandescent and CFL bulbs is 1,000 and 10,000 hours respectively. The purchase price of an incandescent bulb is $0.51 and for the CFL it is $5.88. The cost of electricity is 0.06 $ per kWh

The original cost of the incandescent bulb = 0.51

Cost in the electricity usage of  incandescent bulb = 122  × 0.06  = 7.32

Total cost for 1000 hrs 7.32 + 0.51 = 7.83

Total cost for 10,000  with the use of the incandescent bulb = 78.3

CFL Bulb Is used for 10,000 hrs

The original cost of the CFL = 5.88

Cost associoated with the  Electricity usage of the CFL = 18  * .06 / kWh * 10 kWh = 10.8

Total cost of the CFL = 5.88 + 10.8 = 16.68

78.3 - 16.68 = 61.62

Total savings over the lifetime of CFL would be 61.62 $.

Thus, her total savings over the lifetime of the CFL would be 61.62 $.

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Answer:

t = 0.69R/L

If the resistance R increases, the required time decreases, for the battery reaches a 50% of its initial value.

Explanation:

In order to know what happens to the the time, when the battery reaches a 50% of its initial voltage, while the RL resistance increases, you use the following formula:

\(V=V_oe^{-\frac{R}{L}t}\)            (1)

Vo: initial voltage in the battery

V: final voltage in the battery = 0.5Vo

R: resistance of the RL circuit

L: inductance of the RL circuit

You use properties of logarithms to solve the equation (1) for t:

\(0.5V_o=V_oe^{-\frac{R}{L}t}\\\\ln(0.5)=-\frac{R}{L}t\\\\t=-\frac{L}{R}ln(0.5)=0.69\frac{L}{R}\)         (2)

By the result obtained in the equation (2), you can observe that if the resistance R increases, the required time decreases, for the battery reaches a 50% of its initial value.

Answer:

Two tuning forks with frequencies of 256 Hz and 512 Hz are struck. Which of the sounds will move faster through the air? Neither, the speed of sound is constant in air.

Answer:

To determine the height to which the ball rises before it reaches its peak, we need to know the initial velocity of the ball and the acceleration due to gravity. Let's assume the initial velocity of the ball is v and the acceleration due to gravity is g.

The time it takes for the ball to reach its peak is one-half the total hang-time, or 1/2 * 6.25 s = 3.125 s.

The height to which the ball rises can be calculated using the formula:

height = v * t - (1/2) * g * t^2

Substituting in the values we know, we get:

height = v * 3.125 s - (1/2) * g * (3.125 s)^2

To solve for the height, we need to know the value of v and g. Without more information, it is not possible to determine the height to which the ball rises before it reaches its peak.

Explanation:

Answer:

Approximately \(47.9\; {\rm m}\) (assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\) and that air resistance on the baseball is negligible.)

Explanation:

If the air resistance on the baseball is negligible, the baseball will reach maximum height at exactly \((1/2)\) the time it is in the air. In this example, that will be \(t = (6.25\; {\rm s}) / (2) = 3.125\; {\rm s}\).

When the baseball is at maximum height, the velocity of the baseball will be \(0\). Let \(v_{f}\) denote the velocity of the baseball after a period of \(t\). After \(t = 3.125\; {\rm s}\), the baseball would reach maximum height with a velocity of \(v_{f} = 0\; {\rm m\cdot s^{-1}}\).

Since air resistance is negligible, the acceleration on the baseball will be constantly \(a = (-g) = (-9.81\; {\rm m\cdot s^{-2}})\).

Let \(v_{i}\) denote the initial velocity of this baseball. The SUVAT equation \(v_{f} = v_{i} + a\, t\) relates these quantities. Rearrange this equation and solve for initial velocity \(v_{i}\):

\(\begin{aligned}v_{i} &= v_{f} - a\, t \\ &= (0\; {\rm m\cdot s^{-1}}) - (-9.81\; {\rm m\cdot s^{-2}})\, (3.125\; {\rm s}) \\ &\approx 30.656\; {\rm m\cdot s^{-1}}\end{aligned}\).

The displacement of an object is the change in the position. Let \(x\) denote the displacement of the baseball when its velocity changed from \(v_{i} = 0\; {\rm m\cdot s^{-1}}\) (at starting point) to \(v_{t} \approx 30.656\; {\rm m\cdot s^{-1}}\) (at max height) in \(t = 3.125\; {\rm s}\). Apply the equation \(x = (1/2)\, (v_{i} + v_{t}) \, t\) to find the displacement of this baseball:

\(\begin{aligned}x &= \frac{1}{2}\, (v_{i} + v_{t})\, t \\ &\approx \frac{1}{2}\, (0\; {\rm m\cdot s^{-1}} + 30.565\; {\rm m\cdot s^{-1}})\, (3.125\; {\rm s}) \\ &\approx 47.9\; {\rm m}\end{aligned}\).

In other words, the position of the baseball changed by approximately \(47.9\; {\rm m}\) from the starting point to the position where the baseball reached maximum height. Hence, the maximum height of this baseball would be approximately \(47.9\; {\rm m}\!\).