A projectile of mass 1.350 kg is shot straight up with an initial speed of 22.0 m/s.

(a) How high would it go if there were no air friction?
(b) If the projectile rises to a maximum height of only 17.8 m, determine the magnitude of the average force due to air resistance.

I got the "a" correct with 24.69 m

I need help with part B. I used
F(17.8) = 1/2 (1.350)(22.0)^2 = 18.35 N and it was wrong. I need help with the correct equation to use. Thank you.

(Avg. resistance force) x distance = LOSS of energy, not the initial kinetic energy

Energy loss = Initial KE - M*g*17.8m
= 326.7 J - 235.5 J = 91.2 J

Fav = 5.1 N

To determine the magnitude of the average force due to air resistance, we need to find the work done by air resistance. This can be calculated using the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

However, since the projectile is moving upwards, the work done by the force of gravity needs to be subtracted from the work done by air resistance. This is because the gravitational force is acting in the opposite direction of the motion, while air resistance is acting in the same direction.

The work done by gravity can be calculated as the force of gravity multiplied by the displacement. In this case, the force of gravity is given by the weight of the object, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2). The displacement is equal to the maximum height reached by the projectile, which is 17.8 m.

Therefore, the work done by gravity is: W_gravity = (1.35 kg)(9.8 m/s^2)(17.8 m).

Now, using the work-energy principle, the work done by air resistance can be calculated as the change in kinetic energy. Since the projectile starts with an initial velocity and comes to rest at the maximum height, the change in kinetic energy is equal to the initial kinetic energy. The initial kinetic energy is given by 1/2*m*v^2, where m is the mass (1.35 kg) and v is the initial velocity (22.0 m/s).

So, the work done by air resistance is: W_air = (1/2)(1.35 kg)(22.0 m/s)^2.

Finally, the magnitude of the average force due to air resistance is obtained by dividing the work done by air resistance by the displacement:
Average force = W_air / 17.8 m.

By plugging in the given values, the correct calculations are:
W_gravity = (1.35 kg)(9.8 m/s^2)(17.8 m)
W_air = (1/2)(1.35 kg)(22.0 m/s)^2
Average force = W_air / 17.8 m.

I hope this explanation helps!