1. A 75 kg secret spy skis down a friction-less hill that is 5 m high. At the bo

Question

1. A 75 kg secret spy skis down a friction-less hill that is 5 m high. At the bottom it levels out and he grabs a 25 kg bag of secret ”stuff”. The spy then skis off a 2 m high ledge. How far from the ledge does the spy land?

2. A uranium nucleus (mass 238 u), initially at rest, undergoes radioactive decay. It emits an alpha particle (mass 4 u). The remaining nucleus is thorium (mass 234 u). If the alpha particle is moving at 0.05 × the speed of light (or 5c 100), what is the recoil speed of the thorium nucleus? (Note: u is a unit of mass and does not need to be converted for the problem.)

Explanation / Answer

(1) velocity at the bottom, V = sqrt(2gh) = sqrt ( 2 * 9.8* 5) = 9.89 m/s

At bottom it grabs 25 kg bag. So total mass is 75 + 25 = 100 kg

Time = sqrt ( 2h/g) = sqrt ( 2*2/9.8) = 0.63 sec

Distance = velocity * time = 9.89 * 0.63 = 6.23 m

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