Question

A bullet is fired vertically into the air from the top of building and reaches a height of 1600m. It then falls to the ground below.The total time of flight is 38.0 s.

i) Determine the speed at which the bullet leaves the gun

ii) Determine from what height above the ground is the bullet fired

Determine the speed of the bullet when it hits the ground

Sketch a velocity versus time graph for the motion of the bullet

Answer 1

i) $mgh=mv_0^2/2\to v_0=\sqrt{2gh}=\sqrt{2\cdot9.8\cdot1600}=177(m/s)$ . Answer

ii) $v=v_0-gt\to t=v_0/g=177/9.8=18.1(s)$

$H=gt^2/2=9.8\cdot(38-18.1)^2/2=1940.4(m)$

$h_0=1940.4-1600=340.4(m)$ . Answer

iii) $mgH=mv^2/2\to v=\sqrt{2\cdot9.8\cdot1940.4}=195(m/s)$ . Answer

iv)