To calculate the time it takes for the ball to reach the highest point, you can use the kinematic equation for vertical motion. When the ball reaches the highest point, its final velocity (v_f) will be zero. The initial velocity (v_i) can be determined by assuming the ball was thrown vertically upward with a certain initial speed.
The kinematic equation for vertical motion is:
v_f = v_i + a * t
where:
- v_f is the final velocity (which is zero at the highest point)
- v_i is the initial velocity
- a is the acceleration (acceleration due to gravity, which is approximately -9.8 m/s^2)
- t is the time
In this case, we know that the final velocity is zero at the highest point, so the equation becomes:
0 = v_i - 9.8 * t_h
where t_h is the time taken to reach the highest point.
To find the time it takes to reach the highest point, we can rearrange the equation:
t_h = v_i / 9.8
Now, to calculate the speed of the ball upon arrival back to the ground, we can use the fact that the speed is the same when the ball lands as when it was initially thrown upward. Therefore, the speed at the highest point will be equal to the initial speed (v_i).
Hence, to find the speed of the ball upon arrival back to the ground, you need to determine the initial speed (v_i) with which the ball was thrown upward.
Please provide the value of the initial speed, and I can help you calculate the time to reach the highest point and the speed upon arrival back to the ground.