A stone is 24M high.a stone is projected upward from the tower with an initial velocity of 24,5m/s.
calculate how long it would take for the stone to reach the ground at the foot of the tower.
just solve for t in
24 + 24.5t - 4.9t^2 = 0
To calculate the time it would take for the stone to reach the ground, we can use the equations of motion. Let's break down the problem step by step:
1. Determine the initial velocity (u) of the stone: Given in the problem as 24.5 m/s.
2. Determine the acceleration (a) acting on the stone: Since the stone is projected upwards and eventually returns to the ground, the acceleration due to gravity is acting downwards. On Earth, the acceleration due to gravity is approximately 9.8 m/s^2, so we take a = -9.8 m/s^2 (negative because it is acting in the opposite direction to the initial velocity).
3. Determine the displacement (s) of the stone: Given in the problem as 24 m. To calculate the displacement, we take the negative value because the stone is moving downward.
4. Determine the final velocity (v) of the stone at the ground: When the stone reaches the ground, its final velocity will be 0 m/s.
Now, we can use the second equation of motion to find the time (t) it takes for the stone to reach the ground:
v^2 = u^2 + 2as
Rearranging the equation, we have:
t = (v - u) / a
Substituting the values we have:
t = (0 - 24.5) / (-9.8)
t = 2.5 seconds
So, it would take approximately 2.5 seconds for the stone to reach the ground at the foot of the tower.