When a body is projected horizontally, its initial vertical velocity is zero. The only force acting on the body is gravity, which causes it to accelerate vertically downward.
Using the equations of motion, we can determine the time it takes for the body to hit the ground. Let's assume the acceleration due to gravity is approximately 9.8 m/s² (which is close enough for most practical purposes on Earth). The initial vertical velocity (v₀) is 0 m/s, and the initial vertical displacement (s₀) is 100 m. We need to find the time it takes for the body to reach the ground (t).
We can use the equation for vertical displacement:
s = s₀ + v₀t + 0.5at²
Substituting the known values:
0 = 100 + 0t + 0.5 * 9.8 * t²
Rearranging the equation:
4.9t² = 100
Dividing both sides by 4.9:
t² = 20.41
Taking the square root of both sides:
t = √20.41 ≈ 4.52 s
Now, we can calculate the horizontal velocity (v) with which the body hits the ground. Since there is no horizontal acceleration, the horizontal velocity remains constant throughout the motion. The initial horizontal velocity (v₀) is 9.8 m/s, and the horizontal displacement (s) is not given. However, since the body is projected horizontally, the horizontal displacement is not affected by the vertical motion. Therefore, we can assume the horizontal displacement is the same as the height of the tower, which is 100 m.
We can use the equation for horizontal displacement:
s = v₀t
Substituting the known values:
100 = 9.8 * 4.52
Solving for v:
v ≈ 44.296 m/s
Therefore, the velocity with which the body hits the ground is approximately 44.296 m/s horizontally.