Question

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 =
hints: 4% deduction per hint. hints remaining: 1
2 submission(s) remaining
hint
feedback
i give up!
feedback: 5% deduction per feedback.
grade summary
deductions
potential
submissions
attempt(s) remaining: 2
4% deduction per attempt
1 detailed view

Explanation:

Step1: Recall the kinematic - equation

The kinematic equation is $v = v_0+at$. The time of descent $t_{down}=t_{total}-t_{top}$. The initial velocity for the descent is $0$ (at the top - most point of the trajectory), and the acceleration is $a$. The velocity $v_f$ before hitting the ground can be found using the equation for the descent part. The initial velocity for the whole motion is $v_i$, and we know that for the upward - motion, at the top $v = 0=v_i - at_{top}$, so $t_{top}=\frac{v_i}{a}$. Then $t_{down}=t_{total}-\frac{v_i}{a}$.

Step2: Apply the kinematic equation for the descent

Starting from rest ($v_0 = 0$) at the top and accelerating with $a$ for a time $t_{down}=t_{total}-\frac{v_i}{a}$, using $v = v_0+at$, we get $v_f=a(t_{total}-\frac{v_i}{a})=at_{total}-v_i$.

Answer:

$v_f = at_{total}-v_i$