A bullet fired into a target loses half of its velocity after penetrating 3 cm. How much further will it penetrate before coming to rest, assuming that it faces constant resistance to motion?
Answer (2)
The bullet's kinetic energy just as it hits the target is (1/2) (mass) (speed in air)².
After 3 cm, its speed is reduced to half, so its KE is (1/2) (mass) (1/2 speed in air)². That's only 1/4 of its original KE. It lost 3/4 of its energy so far.
As it tears through the target, the force against it is constant. So the energy taken away from it is (whatever the force is) x (the distance it travels).
It lost 3/4 of its energy in 3 cm. So it's losing 1/4 of its energy each centimeter, and it has only 1 more cm to go before it stops completely.
The bullet will penetrate an additional 1 cm after losing half of its velocity, based on the constant energy loss due to resistance. Initially, it penetrates 3 cm while losing 3/4 of its kinetic energy, and it retains enough energy to penetrate 1 more cm. In total, it will penetrate 4 cm before stopping.
;
