Question #570

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?

Expert's answer

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

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

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