First slide

Projection Under uniform Acceleration

Question

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

Moderate

A

$\frac{R}{4}$
B

$\frac{R}{2}$
C

2R
D

4R

Solution

$\frac{R}{T^{2}} = \frac{u^{2} \sin 2 θ \times g^{2}}{g (4 u^{2} \sin^{2} θ)} = \frac{g}{2} \cot θ$
${i.e., T}^{2} = \frac{2 R}{g} \tan θ$
If T is doubled, then R becomes 4 times.

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