A 33-kg girl is bouncing on a trampoline. During a certain interval after she leaves the
surface of the trampoline, her kinetic energy decreases to 195 J from 425 J. How high
does she rise during this interval? Neglect air resistance.
KE decreased by 230J
PE increased by 230J = mgh
So, find h
adding on to steve its h = 230/30*9.8 = 0.78
To find the height to which the girl rises, we need to determine the potential energy at the maximum height, which can be found using the conservation of mechanical energy principle.
The total mechanical energy is the sum of the kinetic energy (KE) and potential energy (PE):
Total mechanical energy = KE + PE
Initially, when the girl leaves the surface of the trampoline, all her energy is in the form of kinetic energy. At this moment, her kinetic energy is 425 J.
Total mechanical energy (initially) = 425 J
When she reaches the maximum height during the interval, all her kinetic energy is converted into potential energy. At this moment, her kinetic energy is zero, as she is momentarily stationary.
Total mechanical energy (at maximum height) = PE (potential energy)
Finally, her kinetic energy decreases to 195 J during the interval, so the change in mechanical energy is given by:
Change in mechanical energy = Final mechanical energy - Initial mechanical energy
Change in mechanical energy = (PE at maximum height) - 425 J
Change in mechanical energy = 0 - 425 J
Change in mechanical energy = -425 J
Since no energy is lost due to air resistance (neglecting air resistance), the decrease in mechanical energy is due to the increase in potential energy. So:
Change in mechanical energy = Potential energy gain
-425 J = PE
Now, we can find the potential energy gain at the maximum height, which is the same as the change in mechanical energy:
PE = -425 J
The potential energy (PE) is given by the formula:
PE = mgh
Where m is the mass of the girl, g is the acceleration due to gravity, and h is the height.
Given that the mass of the girl is 33 kg and g = 9.8 m/s^2, we can rearrange the formula to solve for h:
h = PE / (mg)
h = -425 J / (33 kg * 9.8 m/s^2)
Now we can calculate the height:
h = -425 J / (323.4 kg m^2/s^2)
h ≈ -1.31 meters
Since height cannot be negative, we take the absolute value and the girl rises to a height of approximately 1.31 meters during the interval.