Can you solve this hard physics question?

Question

A horizontal rifle is fired at a bull's-eye. The muzzle speed of the bullet is 655 m/s. The barrel is pointed directly at the center of the bull's-eye, but the bullet strikes the target 0.049 m below the center. What is the horizontal distance between the end of the rifle and the bull's-eye?

Please explain how to solve this problem in detail!

Answer 1

The bullet is acted upon by gravity which pulls it down and causes it to miss the center. Gravity provides constant acceleration and the formula for distance s in time t with acceleration g is:

s = (1/2)gt^2

We know s and g so this can be used to find the time it takes the bullet to reach the target.

s in this case is 0.049 meters

g is the acceleration of gravity = 9.8 m/s

0.049 = (1/2)(9.8)t^2

t = SQRT[(0.049)(2)/9.8]

t = 0.1 seconds

So the time to reach the target is 0.1 seconds

Since the muzzle speed is 655 m/s, the distance is:

Distance = (0.1)(655) = 65.5 meters

Answer 2

When fired horizontally, a bullet will fall the same amount as if you dropped it, so you can use the normal equations of motion.

1. Find the time as a function of height dropped and g (gravity)

h = ½gt²

t = √2h/g

t = √(2 * 0.049 / 9.8)

t = 0.1 s

2. Calculate the distance:

x = vt

x = 655 * 0.1

x = 65.5 m