Question

If a gun is sighted to hit targets that are at the same height as the gun and 85 m away at the same height, how low, as a positive number in meters, will the bullet hit if aimed directly at a target 180 m away

Answer 1

If a gun is sighted to hit targets that are at the same height as the gun and 85 m away at the same height, how low, as a positive number in meters, will the bullet hit if aimed directly at a target 180 m away

The muzzle velocity of the bullet is 275 m/s

Answer:

y = -1.1109 m

Explanation:

Range = $\frac{v^2sin2\theta}{g}$

range = 85 m

velocity = 275 m/s

g = 9.8 m/s²

$85 = \frac{(275)^2sin2 \theta}{9.8}$

$833=(275)^2sin2\theta$

$833= 75625sin2\theta$

$0.01101 =sin2 \theta$

$0.005505 =sin \theta$

$\theta =sin^{-1}(0.005505)$

$\theta = 0.3154^0$

If the bullet is aimed at a target 180 m, time required to travel 180 m with horizontal component will be;

$t=\frac{180}{275cos0.3154}$

t = 0.6546 sec

To determine, how low as a positive number in meters.

$y=vyt-\frac{gt^2}{2}$

y = $275 sin(0.3154)*(0.6546)-$ $\frac{9.8*(0.6546)^2}{2}$

y = 0.9909 - 2.1018

y = -1.1109 m