First slide

Projection Under uniform Acceleration

Question

A projectile can have the same range R for two angles of projection. If t₁ and t₂ be the times of flights in the two cases, then the product of the two times of flight is proportional to

Moderate

A

R
B

1/R
C

1/R²
D

R²

Solution

Here $t_{1} = \frac{2 usin α}{g} and t_{2} = \frac{2 usin (90^{\circ} - α)}{g} \dots (1)$
Now $t_{1} t_{2} = \frac{4 u^{2}}{g^{2}} \sin αcos α$
We know that
$R = \frac{u^{2} \sin 2 α}{g}$
From eqs. (1) and (2), we get
$t_{1} t_{2} = \frac{2 R}{g} \propto R$

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