A stone is projected horizontally with a velocity of 10m/s from the top of a building 39.2 m high. How long will the stone take to hit the ground.

Sure, let's solve this step by step.

1. First, we need to understand that the stone is projected horizontally. This means that the initial vertical velocity (u) of the stone is 0 m/s.

2. The height (h) from which the stone is projected is given as 39.2 m.

3. We also know that the acceleration due to gravity (g) is approximately 9.8 m/s².

4. We can use the second equation of motion to solve this problem, which is: h = ut + 0.5gt². Since the initial vertical velocity (u) is 0, the equation simplifies to: h = 0.5gt².

5. We can rearrange this equation to solve for time (t): t = sqrt((2h)/g).

6. Substituting the given values into this equation gives: t = sqrt((2*39.2)/9.8) = sqrt(8) = 2.83 seconds.

So, the stone will take approximately 2.83 seconds to hit the ground.