Putu N.

asked • 03/10/16# show that the speed varies with height according to the equation below

A gun is fired straight up. Assuming that the air drag on the bullets varies quadratically with speed,

(1) show that the speed varies with height according to the equations:

- v
^{2}= Ae^{-2}^{kx}- 8/k (upward motion) - v
^{2}= 8/k - Be^{2kx}(downward motion)

g = acceleration of gravicity;

k= C

_{2}/m, C_{2 }is the drag constant;m= mass of bullet.

{Note: x is measured positive upward, and the gravitational force is assumed to be constant.

(2) when the bullets hits the ground on its return, the speed will be equal to expression:

V

_{o}V_{1}/(V_{o}^{2}+V_{1}^{2})^{1/2 }in which Vo is the initial upward speed and

V

_{t}= (mg/C_{2})^{1/2}= terminal speed = (g/k)^{1/2}
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