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Question

The maximum range for a shell fired by a cannon on horizontal terrain is 20 km. What must be the muzzle velocity of the shell? (Take g=10 m/s2)

A
225 m/s
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B
126 m/s
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C
1503 m/s
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D
2005 m/s
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Solution

The correct option is D 2005 m/s
Formula for range is,
R=u2sin2θg

Let the muzzle velocity be u.
For maximum range, numerator should be maximized.
Since speed for fired shell is equal to u m/s every time. (u constant)
Maximum range will correspond to maximum value of sin2θ, which is 1.
sin2θ=12θ=90
Thus, θ=45 should be the angle of firing (angle of projection) for shell to obtain maximum range.

Rmax=u2g
20×103=u210
u=20×104=2005 m/s

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