## Mastering Physics Solutions: A Girl on a Trampoline

A Girl on a Trampoline

Part A = 4.98m/s
Part B = 3.98m/s
Part C = inelastic
Part D = 2.81m

Solutions Below:

A girl of mass m1 = 60 kilograms springs from a trampoline with an initial upward velocity of vi = 8.0 meters per second. At height h = 2.0 meters above the trampoline, the girl grabs a box of mass m2 = 15 kilograms.

For this problem, use g = 9.8 meters per second per second for the magnitude of the acceleration due to gravity.

Part A

What is the speed vbefore of the girl immediately before she grabs the box?

We can solve this using the kinematic equation Vf2 = Vi2 + 2a(d):

Vf2 = Vi2 + 2a(d)
Vf2 = (8.0)2 + 2(-9.8)(2.0)
Vf2 = 64 – 39.2
Vf2 = 24.8

Vf = 4.98m/s

Part B

What is the speed vafter of the girl immediately after she grabs the box?

Since momentum is conserved, we can solve this equation using the formula for momentum (p = mv). Note that since this is an inelastic collision, energy is not conserved, so we won’t be able to solve using the formulas for kinetic and potential energy:

p = mv

Solve for momentum using the velocity (from Part A) just before the girl picks up the box:

p = 60(4.98)
p = 298.8Ns

Now solve for when the box gets picked up:

p = mv
298.8 = (60 + 15)v
298.8 = 75v

v = 3.98m/s

Part C

Is this “collision” elastic or inelastic?

A. elastic
B. inelastic

Since the two objects stick together after colliding, the collision is inelastic:

B. inelastic

Part D

What is the maximum height hmax that the girl (with box) reaches? Measure hmaxmax with respect to the top of the trampoline.

We can solve this using the kinematic equation Vf2 = Vi2 + 2a(d). We know that at the maximum height, gravity will have slowed velocity to zero, and our initial velocity will be from just after the girl picks up the box (from Part B):

Vf2 = Vi2 + 2a(d)
0 = (3.98)2 + 2(-9.8)(d)
0 = 15.84 – 19.6d
15.84 = 19.6d

d = 0.808

Since the girl picked up the box at 2m above the trampoline, we need to add that into the height:

d = 0.808 + 2

d = 2.81m

Tagged with: