The total time in the air is 0.968 s
Explanation:
The motion of the rebounder is a free fall motion, therefore we can use the following suvat equation:
[tex]s=vt-\frac{1}{2}at^2[/tex]
where:
s is the vertical displacement
v is the final velocity
t is the time
a is the acceleration
Here we consider the first half of the rebounder's motion, from the moment he jumps until the moment he reaches the maximum height. Therefore, we have:
s = 114.73 cm = 1.1473 m is the vertical displacement (upward)
v = 0 is the final velocity (the velocity at the top is zero)
[tex]a=g=-9.8 m/s^2[/tex] is the acceleration of gravity (downward)
Solving for t,
[tex]t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(1.1473)}{9.8}}=0.484 s[/tex]
This is the time the rebounder takes to reach the top: the time he takes to fall back down again to the ground is identical, so the total time in the air is
[tex]T=2t=2(0.484 s)=0.968 s[/tex]
Learn more about free fall motion:
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