A child is bouncing an a trampoline. The child has a mass of 42.5 kg . She leave

Question

A child is bouncing an a trampoline. The child has a mass of 42.5 kg . She leaves the surface of the trampoline with an initial upwards velocity of 7.70 m/s . When she reaches height 1.60 m above the trampoline (still on the way up), she grabs a large (stationary) plastic block. The mass of the block is 4.50 kg .

For this problem, use g=9.80 meters per second per second for the magnitude of the acceleration due to gravity.

1.What is the speed vbefore of the child immediately before she grabs the block?

2.What is the speed vbefore of the child immediately before she grabs the block?

3.

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

Explanation / Answer

(A) vf^2 - vi^2 = 2 a d

v^2 - (7.70)^2 = 2(-9.80)(1.60)

v = 5.3 m/s

(b) Applying momentum conservation just before and after child grabs block,

(42.5 x 5.3) + (4.50 x 0) = (42.5 + 4.5) v

v = 4.8 m/s

(C) from this position,

h = v^2 / 2 g = 4.8^2 / (2 x9.8)

h = 1.16 m

H = 1.60 + h = 2.33 m

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