The person's horizontal position is given by
and the time it takes for him to travel 56.6 m is
so your first computed time is the correct one.
The question requires a bit of careful reading, and I think there may be a mistake in the problem. The person's vertical velocity 
at time 
is
which tells us that he would reach the ground at about 
. In this time, he would have traveled
But we're told that he is caught by a net at 56.6 m, which would mean that the net cannot have been placed at the same height from which he was launched. However, it's possible that the moment at which he was launched doesn't refer to the moment the cannon went off, but rather the moment at which the person left the muzzle of the cannon a fraction of a second after the cannon was set off. After this time, the person's initial vertical velocity 
would have been a bit smaller than 
.
Answer: Force applied by trampoline = 778.5 N
<em>Note: The question is incomplete.</em>
<em>The complete question is : What force does a trampoline have to apply to a 45.0 kg gymnast to accelerate her straight up at 7.50 m/s^2? note that the answer is independent of the velocity of the gymnast. She can be moving either up or down or be stationary.
</em>
Explanation:
The total required the trampoline by the trampoline = net force accelerating the gymnast upwards + force of gravity on her.
= (m * a) + (m * g)
= m ( a + g)
= 45 kg ( 7.50 * 9.80) m/s²
Force applied by trampoline = 778.5 N
Closer to the sun . . . orbital speed is faster.
Farther from the sun . . . orbital speed is slower.
Flag answer: Answer 13 Answer 13
It's total kinetic energy
