Painter, wearing roller skates, starts with negligible velocity at the top of th

Question

Painter, wearing roller skates, starts with negligible velocity at the top of the dome and coastst down over the dome's surface. The mass of painter, including skates is 80kg and the radius of the dome is 8m. Assume that the painter's mass is constant over this one run and neglect friction and air resistance.

If the net is removed, what velocity would the painter have when he impacts the ground, what impulse would the ground deliver to the painter in order to stop him and where should the assistant place the net from the dome to break the daredevil's fall?

You guys are truly a lifesaver^^

Explanation / Answer

we have from the law of conservation of energy

(1/2)mv^2 = mgh

v^2/2 = gr

v = (2gr)^(1/2) = 12.5 m/s

The velocity with which the painter impacts to the ground, v = 12.5 m/s

Impulse = change in momentum = final momentum - initial momentum

            initially the velocity is neglisible. So the initial momentum is zero.

            So, the Impulse = Final momentum = mv = 1000 N sec    

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