Question

A boy weighing 15 kg falls from rest and hits the ground. During the collision with the ground, he comes to rest in a time of 0.06 seconds. The average force exerted by the ground was 12,500 N. From what height did the boy fall?

Answer 1

To determine the height from which the boy fell, first calculate the impulse using the average force and time interval. Then determine the velocity before impact using the momentum. Finally, use the conservation of energy to find the initial height with the calculated velocity.

Step-by-step explanation:

Calculating the Height of the Fall Using the Impulse-Momentum Theorem

To find the height from which the boy fell, we'll first calculate the change in momentum, or impulse, which equals the average force exerted by the ground multiplied by the time interval it was applied. The formula for impulse (J) is:

J = FΔt

Where F is the average force and Δt is the time interval. After calculating the impulse, we'll use it to find the boy's velocity just before impact, utilizing the formula for momentum (p):

p = mv

Where m is the mass and v is the velocity. With the final velocity determined, we can then use the conservation of energy to calculate the height from which the boy fell. The kinetic energy just before impact (KE) will equal the potential energy at the initial height (PE), that is:

KE = PE or ½mv² = mgh

Finally, solving for h (height), we get:

h = v² / (2g)

Here, g is the acceleration due to gravity (9.81 m/s²). By plugging in the values, we can find the height the boy fell from.