a stone is dropped from the tower of hight 125m; calcute
(1) Time taken to reach the ground.
(2) Find velocity of stone.
To calculate the time taken for the stone to reach the ground and its velocity, we can use the formulas of motion under gravity.
(1) Time taken to reach the ground:
The time equation for an object in free fall is given by:
h = (1/2)gt^2,
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken.
In this case, the stone is dropped from a height of 125m. To find the time taken to reach the ground, we rearrange the formula:
125 = (1/2) * 9.8 * t^2.
Simplifying the equation:
125 = 4.9t^2.
Dividing both sides by 4.9:
t^2 = 25.51.
Taking the square root of both sides:
t ≈ 5.05 seconds.
Therefore, the time taken for the stone to reach the ground is approximately 5.05 seconds.
(2) Velocity of the stone:
The velocity equation for an object in free fall is given by:
v = gt,
where v is the velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken.
Using the value of time we found earlier (t ≈ 5.05 seconds):
v = 9.8 * 5.05.
Calculating the velocity:
v ≈ 49.49 m/s.
Therefore, the velocity of the stone when it reaches the ground is approximately 49.49 m/s.