Question

A rifle is aimed horizontally at a target 50.0 m away. The bullet hits the target 2.90 cm below the aim point.

Whats the bullet's flight time?
Whats the bullet's speed as it left the barrel?

Answer 1

You can see it like this:
The time it takes the bullet to reach the target is how long it takes it to fall 2.9 cm due to gravity from rest:\[y(t) = 1/2 \times g \times t^{2}\]
You solve that for t and get (assuming g=10 m/s^2) t = 0.076s flight time.

For the speed you now know it flew 50m in 0.076s, and neglecting air friction that gives you 657.9m/s

Answer 2

we could also time how long it take something to drop: .029 meters in free fall.

h(t) = -4.9^2 + .029 = 0
.029 = 4.9 t^2
.029/4.9 = t^2
sqrt(.029/4.9) = t

distance/time = speed; and lets assume the speed is constant.

speed = 50(7)/sqrt(.29)
= 350sqrt(.29)/.29
= 350sqrt(.29)/.29

=abt. 649.934; when we approximate
with the exact time.

Answer 3

the error of course is in how accurate you want to be :)