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 = [tex]\frac{v^2sin2\theta}{g}[/tex]
range = 85 m
velocity = 275 m/s
g = 9.8 m/s²
[tex]85 = \frac{(275)^2sin2 \theta}{9.8}[/tex]
[tex]833=(275)^2sin2\theta[/tex]
[tex]833= 75625sin2\theta[/tex]
[tex]0.01101 =sin2 \theta[/tex]
[tex]0.005505 =sin \theta[/tex]
[tex]\theta =sin^{-1}(0.005505)[/tex]
[tex]\theta = 0.3154^0[/tex]
If the bullet is aimed at a target 180 m, time required to travel 180 m with horizontal component will be;
[tex]t=\frac{180}{275cos0.3154}[/tex]
t = 0.6546 sec
To determine, how low as a positive number in meters.
[tex]y=vyt-\frac{gt^2}{2}[/tex]
y = [tex]275 sin(0.3154)*(0.6546)-[/tex] [tex]\frac{9.8*(0.6546)^2}{2}[/tex]
y = 0.9909 - 2.1018
y = -1.1109 m
