First slide

Projection Under uniform Acceleration

Question

A projectile has same range R for the two angles of projection. If T₁ and T₂ are the times of flight in two cases, then:

Easy

A

$T_{1} T_{2} \propto R$
B

$T_{1} T_{2} \propto R^{2}$
C

$T_{1} T_{2} \propto \frac{1}{R}$
D

$T_{1} T_{2} \propto \frac{1}{R^{2}}$

Solution

Range is same for angle of projection $θ and (90 - θ)$
$\begin{array}{l} T_{1} T_{2} = \frac{2 usin θ}{g} \cdot \frac{2 usin (90 - θ)}{g} \\ T_{1} T_{2} = \frac{4 u^{2} \sin θcos θ}{g^{2}} \\ \frac{2}{g} \cdot \frac{u^{2} \sin θ}{g} = \frac{2 R}{g} \\ \Rightarrow T_{1} T_{2} \propto R \end{array}$
Hence correct choice is (1).

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