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A gun shoots a bullet with a velocity of magnitude 464 m/s. The goal is to hit the target 1,092 meters away. How high above the target must you aim to correct for gravity? (Assume the gun and target are at the same eight)

Question
A gun shoots a bullet with a velocity of magnitude 464 m/s. The goal is to hit the target 1,092 meters away. How high above the target must you aim to correct for gravity? (Assume the gun and target are at the same eight)
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Step 1

Draw the figure. Consider A to be the position from which the bullet is shot, B to be the position of the target and C to be the aiming position. The bullet is fired with an initial speed u, making an angle θ with the horizontal axis. Thus, the initial speed will have two components; one along the horizontal axis and the other along the vertical axis.

クK、
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クK、

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Step 2

Upon applying Newton’s equation for motion, the expression for the distance covered by the bullet is:

u2sin 20
D =
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u2sin 20 D =

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Step 3

Substitute 1092 m for D, 464 m/s for u and 9.8 m/s2 for ...

(1092 m(464 m s
1sin 20
(9.8 m-s2)
sin 20 0.05
20 sin(0.05
-1
0 1.43
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(1092 m(464 m s 1sin 20 (9.8 m-s2) sin 20 0.05 20 sin(0.05 -1 0 1.43

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Physics

Kinematics

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