During a circus performance, a 73.1-kg human cannonball is shot out of a 19.5-m-long cannon. If the human cannonball spends 0.921 s in the cannon, determine the average net force exerted on him in the barrel of the cannon.

His average speedm in the cannon is

Vav = 19.5/0.921 = 21.17 m/s

The exit velocity is twice that, or
Vfinal = 42.35 m/s

For the accleration,
a = Vfinal/0.921s = 46.0 m/s^2

The average force (in newtons) is the mass (in kg) times the acceleration.

To determine the average net force exerted on the human cannonball in the barrel of the cannon, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Let's break down the problem and find the necessary information:
- Mass of the human cannonball (m): 73.1 kg
- Length of the cannon (d): 19.5 m
- Time spent in the cannon (t): 0.921 s

First, we need to find the acceleration of the human cannonball in the barrel using the kinematic equation:

d = ut + 0.5at^2

Where:
- d is the distance traveled (19.5 m),
- u is the initial velocity (0 m/s) since the cannonball starts from rest,
- a is the acceleration (unknown),
- t is the time spent in the cannon (0.921 s).

Rearranging the equation to solve for acceleration (a), we get:

a = (2d) / t^2

Plugging in the values, we have:

a = (2 × 19.5 m) / (0.921 s)^2

Now we have the acceleration of the human cannonball in the barrel.

Next, we can calculate the net force using Newton's second law of motion:

F = m × a

Plugging in the values, we have:

F = 73.1 kg × a

By substituting the calculated value of acceleration (a) into the equation, we can find the average net force exerted on the human cannonball in the barrel of the cannon.