Answer :
When a ball is dropped and bounces, its motion can be analyzed using equations of motion. By finding the time it takes for the ball to reach the ground and the time for its upward motion, we can calculate the maximum height reached after bouncing. In this case, the maximum height is approximately 0.725m.
The maximum height reached by a ball after bouncing can be determined by analyzing its vertical motion. When a ball is dropped from a height and bounces back, it goes through a series of upward and downward motions. To find the maximum height reached after bouncing, we need to calculate the time it takes for the ball to reach the ground and then use this time to find the height reached during the upward motion.
In this case, the initial height of the ball is 10m. Using the equation y = yo + voyt - 1/2gt[tex]^{2}[/tex], where yo is the initial height, voy is the initial vertical velocity (which is zero in this case), g is the acceleration due to gravity, and t is the time, we can find the time it takes for the ball to reach the ground. Using the quadratic formula, we find two values for t: 3.79s and 0.54s. Since the ball reaches a height of 10m twice during its trajectory, we take the longer time of 3.79s. This means that the ball spends 3.79s in the air.
Now, to find the maximum height reached after bouncing, we need to find the height reached during the upward motion. Since the ball spent 3.79s in the air, the time for the upward motion is half of that, which is 1.895s. Using the same equation, but with a positive value for the acceleration due to gravity since it is acting opposite to the motion, we can calculate the height reached during this time.
Substituting the known values,
we get y = 10 + 0*t - 1/2*(9.8)*(1.895)[tex]^{2}[/tex]
= 10 - 1/2*(9.8)*(1.895)[tex]^{2}[/tex]
= 10 - 1/2*18.55
= 10 - 9.275
= 0.725m.
Correct Question
A ball is dropped from a height of 10m above the ground. What is the maximum height reached by the ball after bouncing?
