A projectile has a time of flight $T$ and range $R$ . If the time of flight is doubled, keeping the angle of projection same, what happens to the range?

R / 4

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R / 2

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2 R

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4 R

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Solution

The correct option is D $4 R$
$\frac{R}{T^{2}} = \frac{u^{2} sin 2 θ / g}{4 u^{2} {sin}^{2} θ / g^{2}} = \frac{g}{2} cot θ$
i.e., $g T^{2} = 2 R tan θ$
If $T$ is doubled, then $R$ becomes $4$ times.

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A projectile has a time of flight T and range R. If the time of flight is doubled, keeping the angle of projection same, what happens to the range?

The correct option is D 4RRT2=u2sin2θ/g4u2sin2θ/g2=g2cotθi.e., gT2=2RtanθIf T is doubled, then R becomes 4 times.

A projectile has a time of flight $T$ and range $R$ . If the time of flight is doubled, keeping the angle of projection same, what happens to the range?

The correct option is D $4 R$
$\frac{R}{T^{2}} = \frac{u^{2} sin 2 θ / g}{4 u^{2} {sin}^{2} θ / g^{2}} = \frac{g}{2} cot θ$
i.e., $g T^{2} = 2 R tan θ$
If $T$ is doubled, then $R$ becomes $4$ times.