Question

part (d) what is the maximum height the ball reaches in meters? (h_{max}=3.265 m) correct! part (e) enter an expression for the elapsed time it takes for the ball to travel from the ground to a given height (h), and the acceleration (a). (delta t = v_i - sqrt{v_i^2 - 2ah}/a) incorrect! part (f) how long does it take the ball to reach its maximum point (t_{top}) in seconds? (t_{top}=0.8160 s) correct! part (g) what is the total displacement, in meters, of the ball for its entire motion: traveling from the ground to the top and then returning to the ground? (delta y_{total}=0.0000 m) correct! part (h) enter an expression for the total time of flight of the ball: the time from when it is launched to when it lands back on the ground. express this time in terms of (v_i) and (a). (t_{total}=-2v_i/a) correct! part (i) calculate the value of (t_{total}) in seconds. (t_{total}=1.632 s) correct! part (j) enter an expression for (t_{total}) in terms of the variable (t_{top}), the time of ascent from the ground to the top of the trajectory.

Explanation:

Step1: Analyze motion - up and down symmetry

In vertical - motion under constant acceleration (free - fall), the time of ascent is equal to the time of descent. If \(t_{top}\) is the time to reach the maximum height, the total time of flight \(t_{total}\) is related to \(t_{top}\) by the fact that the motion is symmetric.

Step2: Determine the expression for total time

Since the time going up is the same as the time coming down, the total time of flight \(t_{total}=2t_{top}\).

Answer:

\(t_{total} = 2t_{top}\)