Question

If a gun is sighted to hit targets that are at the same height as the gun and 95 m away, how low will the bullet hit if aimed directly at a target 195 m away? the muzzle velocity of the bullet is 275 m/s.

Answer 1

Horizontal distance between the bullet and the target (s) = 195 m

Horizontal velocity of the bullet (u) = 275 m/s

Time taken to cover the horizontal distance = $\frac{Distance}{velocity}$

Time taken (t) = $\frac{195}{275}$

t = 0.709 s

Now, in the vertical direction:

Initial velocity (u) = 0 m/s

Let the depth covered be h.

Time taken (T) = 0.709 s

Acceleration due to gravity (g) = 9.8 m/s^2

Now, using the seconds equation of motion:

$h = ut + \frac{1}{2}at^2$

$h = 0 +\frac{1}{2}\times 9.8 \times 0.709^2$

h = 2.463 meters

Hence, the bullet will hit 2.463 meters below the target.