Question

• 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 return
δy_total = 0.000 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 groun
a.
t_total=-2 v_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.
t_total = 2 t_top √ correct!

• part (k)

express the velocity of the ball in the instant of time before it hits the ground, v_f, in terms of v_i, t_total, and a.
v_f=(a t_total)-v_i x incorrect!
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part (l)
what is the velocity of the ball, in meters per second, in the instant of time when it returns to the ground?
v_f =

m/s

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Explanation:

Step1: Recall the kinematic - equation

The kinematic equation for velocity is $v_f=v_i + at$. Here, the initial velocity is $v_i$, the acceleration is $a$ (acceleration due to gravity, usually $a=-g$ for upward - motion problems where the positive direction is upward), and the time of flight is $t_{total}$.

Step2: Substitute values

Substituting into the equation $v_f = v_i+at$, we get $v_f=v_i + a t_{total}$. In the case of a ball thrown vertically upwards and coming back to the same position, if we take the upward direction as positive and the acceleration due to gravity $a=-g$ (where $g = 9.8\ m/s^2$), the correct expression for the final velocity $v_f$ in terms of initial velocity $v_i$, total time $t_{total}$ and acceleration $a$ is $v_f=v_i+at_{total}$.

Answer:

$v_f = v_i+at_{total}$