projectile of mass?

Question

a projectile of mass 0.750 kg is shot straight up with an initial velocity of 18.0 m/s. if the projectile rises to a maximum height of only 11.8 m, determine the magnitude of the average force due to air resistance.
a. 8.3 N
b. 2.9 N
c. 11 N
d. 7.4 N
e. 1.5 N

Answer 1

This is not a very challenging one. You know the initial kinetic energy (1/2 m v^2) and the final potential energy (m g h). If you were to take initial kinetic energy - final potential energy you will get some remainder, the work done by air resistance. Work is defined as an average force applied times a distance traveled,W = F d. We know the distance traveled is h, so F = W/h. So I get the final equation:

F = (1/2 m v^2 - m g h)/h = m (1/(2 h) v^2 - g) = 2.9 N

Answer 2

You have the initial kinetic energy, which is converted to potential energy and heat caused by air resistance.

Since you're given the maximum height, you can figure out the potential energy, the rest is lost through air resistance.