A stone is projected vertically upward with a speed of 30m/s from the top of a tower of height 50m neglecting air resistance. Determine the maximum height reached from the ground
To determine the maximum height reached by the stone, we need to use the equations of motion. The key concept to understand is that the maximum height is reached when the final velocity of the stone becomes zero at the highest point of its trajectory.
First, let's analyze the given information:
Initial velocity (u) = 30 m/s (upward)
Final velocity (v) = 0 m/s (at the maximum height, when the stone momentarily stops)
Acceleration (a) = -9.8 m/s^2 (negative because it acts in the opposite direction to the initial velocity, due to gravity)
Displacement (s) = ?
Time taken (t) = ?
Using the second equation of motion, we can determine the time it takes for the stone to reach its maximum height:
v = u + at
0 = 30 - 9.8t
Solving for time (t):
9.8t = 30
t = 30 / 9.8
t ≈ 3.06 seconds
Now, we can use this time to calculate the displacement (maximum height) using the first equation of motion:
s = ut + (1/2)at^2
s = 30 * 3.06 + (1/2) * (-9.8) * (3.06)^2
s ≈ 92.4 - 45.8 ≈ 46.6 meters
Therefore, the maximum height reached by the stone from the ground is approximately 46.6 meters.
Hi = 50
Vi = 30
v = Vi - 9.81 t
at top v = 0
so
t = 30/9.81 = 3.06 seconds to top
h = Hi + Vi t - 4.9 t^2
h = 50 + 30(3.06) - 4.9(3.06)^2