The speed of projection of a projectile is increased by 5%, without changing the angle of projection. The percentage increase in the range will be

2.5%

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7.5%

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10%

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Solution

The correct option is D
10%

We know that, $R = \frac{u^{2} s i n 2 θ}{g}$
When the speed of projection is increased by 5%, $u^{'} = 1.05 u$
So, $R^{'} = \frac{(1.05 u)^{2} s i n 2 θ}{g} = \frac{1.1025 u^{2} s i n 2 θ}{g} = 1.1025 R$
$R^{'}$ is approximately $1.1 R$ .
Now, percentage increase in range $= \frac{1.1 R - R}{R} \times 100 = 10$ %
Thus, the correct choice is (d).

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The speed of projection of a projectile is increased by 5%, without changing the angle of projection. The percentage increase in the range will be

The correct option is D 10% We know that, R=u2 sin 2θg When the speed of projection is increased by 5%, u′=1.05 u So, R′=(1.05 u)2 sin 2θg=1.1025 u2 sin 2θg=1.1025 R R′ is approximately 1.1 R. Now, percentage increase in range =1.1 R−RR×100=10% Thus, the correct choice is (d).