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A bullet is fired with a speed of 1500 m...

A bullet is fired with a speed of 1500 m/s in order to hit a target 100 m away. if `g 10 m//s^(2)`, the gun should be aimed:

A

15 cm above the target

B

10 cm above the target

C

3 cm above the target

D

directly towards the target

Text Solution

Verified by Experts

The correct Answer is:
C
Let the gun be fired with a veocity u at an angle `theta` with the horizontal. Therefore, to hit the target at A, the gun should be aimed at a height AB =h we have,

`OA=R=(u^(2) sin 2 theta)/(g)`
`or sin 2 theta=(Rg)/(u^(2))=(100xx10)/((1500)^(2))=(1)/(2550)`
`:. 2 theta= sin^(-1)(1)/(2250)=0.025^(@)`
`or theta= 0.0.125^(@)=((0.0125xxpi)/(80))^(c)`
`or theta =(2.21xx10^(-4))^(c)`
But `theta=(AB)/(OA)`
Or `AB=theta x OA=(2.21xx10^(-4)xx100)`
`=(2.21xx10^(-2))m`
`=2.21xx10^(-2)xx10^(2) cm`
`=2.21 cm =3 cm`
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