To calculate the height of the wall, we can use the formula for projectile motion:
horizontal distance = initial horizontal velocity * time
In this case, the stone is thrown horizontally, so the initial vertical velocity is 0 m/s. The vertical distance traveled by the stone will be equal to the height of the wall. The horizontal distance traveled by the stone is 45 m, and the initial horizontal velocity is 15 m/s.
Using the formula for horizontal distance, we can rearrange it to solve for time:
time = horizontal distance / initial horizontal velocity
Plugging in the values, we have:
time = 45 m / 15 m/s time = 3 s
Now, we can use the formula for vertical distance to calculate the height of the wall:
vertical distance = initial vertical velocity * time + (1/2) * acceleration * time^2
Since the initial vertical velocity is 0 m/s and the acceleration due to gravity is 10 m/s², the formula simplifies to:
vertical distance = (1/2) * acceleration * time^2
Plugging in the values, we have:
vertical distance = (1/2) * 10 m/s² * (3 s)^2 vertical distance = (1/2) * 10 m/s² * 9 s² vertical distance = 45 m
Therefore, the height of the wall is 45 meters.