Thalia climbs on a swing which is at 0.593 m above ground. Her father pulls back

Question

Thalia climbs on a swing which is at 0.593 m above ground. Her father pulls back the swing to a height of 1.34 m above ground and pushes so that its initial speed is 3.35 m/s. The combined mass of Thalia and swing is 30.8 kg. At the lowest point of the motion, Thalia reaches down and grabs her knapsack of mass 10 kg that is lying on the ground. Note: Neglect air resistance and assume that the swing is frictionless.

1) Find how high above the ground Thalia, swing and knapsack will rise. (meters)

2) After reaching maximum height, Thalia swings backwards and when she reaches the lowest point of the motion, she simply lets go of her knapsack that drops to the ground. Find the maximum height that Thalia and swing reach on the backward swing.

Explanation / Answer

1)

conserving the energy ,
m*gh + 1/2 mv^2 = (m+M)gh'

30.8 * 9.81 * 1.34 + 1/2 * 30.8* 3.35^2 = ( 30.8+10)*9.81 * h '

so,
the height , Thalia will gain ,
h' = 1.443 m

b)
again conserving ,
( 30.8+10)*9.81 * 1.443 = 30*9.81* h

so ,
final height she will gain,

h = 1.962 m

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