First slide

Projection Under uniform Acceleration

Question

Two particles are projected in air with speed u at angles $θ_{1} a n d θ_{2}$ (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?

Moderate

A

$θ_{1} > θ_{2}$
B

$θ_{1} = θ_{2}$
C

$T_{1} < T_{2}$
D

$T_{1} = T_{2}$
where $T_{1} and T_{2}$ are the time of flight.

Solution

Height H = $\frac{u^{2} \sin^{2} θ}{2 g}$
For the same speed
$H \propto \sin^{2} θ$
$∵ H_{1} > H_{2} (Given)$
$∴ {sin}^{2} θ_{1} {> sin}^{2} θ_{2}$
or $θ_{1} > θ_{2}$ ----------(i)
Time of flight, T = $\frac{2 u sinθ}{g}$
For the same speed
T $\propto \sin θ$
$θ_{1} > θ_{2} (From (i))$
$∴ {sin θ}_{1} {> sin θ}_{2} {⇒ T}_{1} {> T}_{2}$

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