Average Resistance Force Question

[alexandray77]

Our question to solve is:
A 5.2 g Ball bearing is fired vertically downward from 18m with an initial speed of 14 m/s. It buries itself a depth of 21 cm in the sand. What average resistance force does the sand exert on the ball bearing?

We know the answer is -6.81N but we are having a hard time figuring out which equations to use to solve the problem. Please help! Thanks!

 

[Rake-MC]

You can use either constant acceleration formulae or conservation of energy to solve this problem.

With constant acceleration you are going to want to calculate the velocity of the ball at the instant it hits the ground. You will then have initial and final velocity and displacement. You can solve for a, and use F = ma to solve for F.With energy, you can use: $$\frac{1}{2}mv_1^2 + mg\Delta h_1 + F_1\Delta d_1 = \frac{1}{2}mv_2^2 + mg\Delta h_1 + F_2\Delta d_2$$
some of these terms will be zero, you are solving for F₂

 

[alexandray77]

thank you!