Answer to Question #304256 in Mechanics | Relativity for Pretty

Question

1.     A summersault swimmer stands on a high platform jumps vertically upward with a velocity of magnitude 2.5 m/s. Air resistance maybe ignored.

a.)   At what time after moving from the platform does the swimmer have a velocity of 0.25 m/s upward?

b.)   At what time does she has a velocity of 0.25 m/s downward?

c.)   When is the displacement of the swimmer from its initial position zero?

d.)   When is the velocity of the swimmer zero?

e.)   What are the magnitude and direction of the acceleration while the swimmer is

i.)                Moving upward?  

ii.)              Moving downward?

Answer 1

Explanations & Calculations

1)

• Since the motion is under gravitational acceleration, apply $\small v=u+at$ upwards for his motion.

$\qquad\qquad \begin{aligned} \small\uparrow 0.25&=\small 2.5ms^{-1}+(-9.8\,ms^{-2})t_1\\ \end{aligned}$ time can be calculated.

2)

• Apply the same formula with signed used correctly,

$\qquad\qquad \begin{aligned} \small \downarrow0.25&=\small -2.5ms^{-1}+(+9.8ms^{-1})t_2 \end{aligned}$ time can be calculated.

3)

• That is when she has returned to the level she started where the displacement in either up or down is zero. So, apply this concept in the formula $\small s=ut+1/2at^2$ to calculate the time for that event.

$\qquad\qquad \begin{aligned} \small \uparrow\\ \small 0&=\small 2.5t_3+\frac{1}{2}(-9.8)t^2_3\\ \small 0&=\small t_3(2.5-0.49t_3)\\ \small t&=\small \begin{cases} 0\,s\\ 0.5\,s \end{cases} \end{aligned}$

• t = 0 refers to the starting moment and t = 0.5 s refers to the moment of returning.

4)

• Velocity becomes zero at the highest point of the trajectory and to calculate the time for that apply $\small v=u+at$ upwards from the start.

$\qquad\qquad \begin{aligned} \small \uparrow 0&=\small 2.5+(-9.8)t_4 \end{aligned}$ time can be calculated.

5)

• Since she moves in freefall under gravity her acceleration is $\small g =9.8 \,ms^{-2}$ . This acceleration is always positioned downwards nevertheless how a body moves. That is why we have a sign conversion giving + and - from time to time we do calculations and that is just to align the direction of gravity as our need/ to get correct calculations.