PHYSICS PRACTICE PROBLEM-NEED HELP FOR EXAM COMING UP

Question

A frog jumps straight up with an initial vertical velocity of 2.5 m/s. Ignoring air resistance, from the time it leaves the ground how long does it take the frog to return to the ground AND what is the total distance the frog traveled?

Answer 1

v_o = 2.5 m/s is the initial vertical velocity

At the top of the jump the frog's velocity is v = 0.

How long does it take?

We us v = 0 = v_o – gt_up to find the time it takes to reach the top of the jump. Solving for t_up gives

t_up = v_o/g = 2.5/9.8 = 0.255 s

It takes the same amount of time to return to the ground as it took the from to get to the top of the jump.

So the total time from the start of the jump to the return to the ground is

t = 2t_up = 2(0.255) = 0.510 s

How far?

To find the maximum height that the frog jumps we use v² = 0 = v_o² – 2gh. Solving for h give

h = v_o²/(2g) = (2.5)²/(2×9.8) = 6.25/19.6 = 0.3289 m

It's the same distance back to the ground, so the total distance the frog travels is

2(0.3289) = 0.6378 m

Answers (rounded to 2 significant figures)

from the time it leaves the ground it take the frog 0.51 s to return to the ground.

the total distance the frog travels is 0.64 m