The initial velocity of the stone can be found using the formula v = d/t, where v is the velocity, d is the distance, and t is the time. In this case, the distance is 165m and the time is 4s, so the initial velocity is 41.25 m/s.
The horizontal distance traveled by the stone can be calculated using the formula d = vt, where d is the distance, v is the velocity, and t is the time. In this case, the velocity is 41.25 m/s and the time is 4s, so the horizontal distance traveled is 165m.
The acceleration of the stone can be found using the formula a = (vf - vi)/t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time. In this case, the final velocity is 0 m/s, the initial velocity is 41.25 m/s, and the time is 4s. Therefore, the acceleration is -10.3125 m/s^2, assuming the stone is thrown upwards.
The maximum height reached by the stone can be calculated using the formula h = vi*t + (1/2)*a*t^2, where h is the height, vi is the initial velocity, t is the time, and a is the acceleration. In this case, the initial velocity is 41.25 m/s, the time is 4s, and the acceleration is -10.3125 m/s^2. Plugging these values in, the maximum height reached by the stone is 66.5m.
The time it takes for the stone to reach the ground can be found using the formula t = sqrt(2h/a), where t is the time, h is the height, and a is the acceleration. In this case, the height is 165m and the acceleration is -10.3125 m/s^2. Plugging these values in, we get a time of 6.42s, which is the total time the stone takes to go up and come back down.