Given:
u = 10⁵ m/s, the entrance velocity
v = 2.5 x 10⁶ m/s, the exit velocity
s = 1.6 cm = 0.016 m, distance traveled
Let a = the acceleration.
Then
u² + 2as = v²
(10⁵ m/s)² + 2*(a m/s²)*(0.016 m) = (2.5 x 10⁶ m/s)²
0.032a = 6.25 x 10¹² - 10¹⁰ = 6.24 x 10¹²
a = 1.95 x 10¹⁴ m/s²
Answer: 1.95 x 10¹⁴ m/s²
By using Ohm's law, we can find what should be the resistance of the wire, R:

Then, let's find the cross-sectional area of the wire. Its radius is half the diameter,

So the area is

And by using the resistivity of the Aluminum,

, we can use the relationship between resistance R and resistivity:

to find L, the length of the wire:
The answer to your question is A
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
.
If the box is moving at constant velocity, net force must be zero, so:
F + fr = 0
fr = -F
<u>fr = -40 N</u>