Question

A piano is suspended 3.6m above the ground and is being raised to apartment 50m high with constant speed of 0.62m/s, after piano has been moving upward for 3.5s coffee cup falls from apartments window onto piano. At what height above the ground is the piano when the cups strikes?

Answer 1

We can find the height of the piano above the ground at the moment when the cup strikes next way:
1) height of the piano (above the ground) after 3.5s of raising: 3.6m + 0.62m/s*3.5s = 5.77m
2) remaining distance: s = 50 - 5.77 = 44.23m
3) equation for the time needed for the cup and piano to hurtle together: s = v*t + 0.5*g*t^2
=> t = (sqrt(v^2 + 2*g*s) - v)/g
=> t = (sqrt(0.62^2 + 2*9.81*44.23) - 0.62)/9.81 = 2.94 (s)
4) height of the piano after more 2.94s of raising: 5.77m + 0.62m/s*2.94s = 7.59m
Answer: 7.59m