A ball is dropped from height of 8m above the ground. After striking the ground the ball rebound instantaneously with the same speed it struck the ground. The instant at which ball strike ground, another ball is drop from the same height. Find the height in metres at which the 2 ball collide. neglect air resistance and size
To find the height at which the two balls collide, we need to determine the time it takes for the first ball to reach the ground and calculate how far the second ball has fallen during that time.
1. Find the time it takes for the first ball to hit the ground:
Using the equation for gravitational free fall, we can solve for the time it takes for the ball to drop from a height of 8m. The equation is given by:
h = (1/2) * g * t^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
8 = 0.5 * 9.8 * t^2
Simplifying the equation, we get:
16 = 9.8 * t^2
t^2 = 16 / 9.8
t = sqrt(1.6327)
t ≈ 1.28 seconds
2. Calculate the distance the second ball falls during this time:
The distance fallen by the second ball is given by the equation d = (1/2) * g * t^2, where d is the distance fallen and t is the time. Since both balls start falling from the same height, we can subtract the distance fallen by the second ball from the original height (8m) to find the collision height.
d = 0.5 * 9.8 * (1.28)^2
d ≈ 8.071m
Therefore, the height at which the two balls collide is approximately 8.071m above the ground.