From the top of a tower is an object with mass 25 kg which is lowered with ropes at a constant speed, 4 m / s to the ground. After 10 seconds the rope by which an object falls freely. From the moment there are 12 seconds to those standing on top of the tower hears the sound of the object hit the ground.

Question

The speed of sound is 334 m / s
Need help setting up the equation for determining the height of the tower.

Answer 1

I thought I set this up for you yesterday.

Let H be the distance above ground from which the object is dropped. The height of the tower is H + 40, since it is dropped and falls freely after being lowered 40 meters.

The time to hear the sound is 12 s after it starts falling freely, according to your statement of the problem.

12 = (H + 40)/334 + (2H/g)^1/2
= H/334 + 0.12 + (2H/g)^1/2

This will result is a very large value for H, about 1200 m. There are no buildings that tall anywhere in the world. I believe you may have stated question incorrectly in English. It would make more sense if the 12 seconds began with the lowering of the object at 4 m/s. Then, only an additional 2.0 seconds would be required for the sound of ground impact to be heard.

Answer 2

Thanks for the answer