Final answer:
The average net force exerted on the performer while being accelerated inside the cannon is 2444.81 N.
Step-by-step explanation:
To find the average net force exerted on the performer while being accelerated inside 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. In this case, the performer's mass is given as 82.6 kg and the speed at which they leave the cannon is 16.4 m/s.
The acceleration can be found by using the equation of motion, v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance travelled. The initial velocity is 0 m/s since the performer starts from rest inside the cannon, and the distance travelled inside the cannon is given as 9.29 m. Solving for the acceleration, we get:
a = (v^2 - u^2) / (2s) = (16.4^2 - 0^2) / (2 * 9.29) = 29.821 m/s^2
Now we can calculate the average net force using the formula:
F = ma = 82.6 kg * 29.821 m/s^2 = 2444.81 N.
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