Question

A rifle is aimed horizontally at a target 31 m away. The bullet hits the target 1.3 cm below the aiming point. Neglect air resistance.
(a) What is the bullet's time of flight?


s

(b) What is its muzzle velocity?


m/s (in the bullet's initial horizontal direction)

Answer 1

a. d = 0.5g*t^2 = 0.013 m.
4.9t^2 = 0.013t^2
t^2 = 0.00265
Tf = 0.052 s. = Fall time or time in flight.

b. Xo * T = 31 m.
0.052Xo = 31
Xo = 602 m/s.

Answer 2

x=x0+v0xt+(1/2)axt^2
=> -0.013~0+0+(1/2)(-9.8)t^2
=> 0.013~(1/2)(9.8)t^2
=> 0.013~4.9t^2
=> t~0.052s
y=y0+v0yt+(1/2)ayt^2
=> 31~0+v0yt+(1/2)(0)(0.052)^2
=> 31~v0yt
=>v0y~31/t
=>v0y~31/.052
=>v0y~6.0*10^2m/s