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A bulley with muzzle velocity 100 m s^-1...

A bulley with muzzle velocity `100 m s^-1` is to be shot at a target `30 m` away in the same horizontal line. How high above the target must the rifle be aimed so that the bullet will hit the target ?
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Text Solution

Verified by Experts

Horizontal range of bullet is `30 m`.
Using range formula, `R = (u^2 sin 2 theta)/(g) = 30`
or `sin 2 theta = (30 xx 10)/((100)^2) or sin 2 theta = 0.03`
For small `theta, sin theta ~~ theta ~= tan theta, i.e., 2 theta = 0.03`
Therefore, `theta = 0.015 rad`
In `Delta OAP, tan theta = (AP)/(OP) rArr AP = OP tan theta`
The rifle must be aimed at an angle `theta = 0.015` above horizontal.
Height to be aimed `= 30 tan theta ~~ 30(theta) = 30 xx 0.015 = 45 cm`.
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