A 150-gram Velcro-dart, travelling horizontally at a speed of 10.0 m/s, hits a f

Question

A 150-gram Velcro-dart, travelling horizontally at a speed of 10.0 m/s, hits a fuzz-ball at rest, hanging from a twine attached to the ceiling, and sticks to it. If the speed of the dart and the ball is 7.00 m/s immediately after impact, the mass of just the fuzz-ball is closest to: A) 64.3 g (B) 100 g (C) 150 g (D) 225 g (E) 350 g (F) 600 g After the Velcro-dart hits and sticks to the fuzz-ball in problem 5, they jointly swing on the twine hanging from the ceiling to a height from the ball's initial position that closest to: (A) 20.0 cm (B) 50.0 cm (C) 80.0 cm (D) 1.30 m (E) 1.80 m (F) 2.50 m

Explanation / Answer

Using energy conservation:

KEi + PEi = KEf + PEf

KEf = 0, since at top swing position vf = 0,

PEi = 0, since potential energy is zero at refrence point

KEi = PEf

0.5*M*V^2 = M*g*h

h = V^2/2g

h = 7^2/(2*9.81) = 2.49 m

Correctoption is F.

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