A 34-kg girl is bouncing on a trampoline. During a certain interval after leaving the surface of the trampoline, her kinetic energy decreases to 220 J from 480 J. How high does she rise during this interval? Neglect air resistance.
KE + PE = 480 Joules
220 + PE = 480
PE = PE = 260 J.
mg*h = 260
34*9.8*h = 260
333.2h = 260
h = 0.780 m.
To determine how high the girl rises during this interval, we need to calculate the change in potential energy.
The change in kinetic energy is given by:
ΔKE = KE_final - KE_initial
From the problem statement, we know that the initial kinetic energy (KE_initial) is 480 J and the final kinetic energy (KE_final) is 220 J.
ΔKE = 220 J - 480 J
= -260 J
Since no other external forces are acting on the girl (neglecting air resistance), this change in kinetic energy is equal to the change in potential energy.
ΔPE = -260 J
The potential energy (PE) can be calculated using the formula:
PE = mgh
Where:
m = mass (34 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height
Rearranging the formula, we can isolate the height (h):
h = ΔPE / (mg)
Substituting the given values:
h = (-260 J) / (34 kg * 9.8 m/s^2)
Calculating the expression:
h = -0.76 m
Since height cannot be negative, the girl rises approximately 0.76 meters during this interval.