Question

Robebobeccoba fires a bullet from a gun while aiming at a target 149 m away. If the

bullet misses the target by 1 m, what is the horizontal velocity of the bullet?

Answer 1

329.6 m/s

Step-by-step explanation:

The bullet has a projectile motion, consisting of two separate motions:

- A horizontal motion with constant velocity

- A free fall motion (constant acceleration) in the vertical direction

The bullet misses the target vertically by 1 m: this means that 1 m is the vertical dispalcement of the bullet. So we can find the total time of the flight by using the suvat equation

`s=ut+(1)/(2)at^2`

where

s = 1 m is the vertical displacement

u = 0 is the initial vertical velocity

`a=g=9.8 m/s^2` is the acceleration due to gravity

t is the time

Solving for t,

`t=\sqrt{(2s)/(a)}=\sqrt{(2(1))/(9.8)}=0.452 s`

The horizontal motion is at constant speed, which is given by

`v_x = (d)/(t)`

where

d = 149 m is the distance covered by the bullet

t = 0.452 s is the time taken

Substituting,

`v_x = (149)/(0.452)=329.6 m/s`