First slide

Projectile motion

Question

The equations of motion of a projectile are given by $x = 36 t m$ and $2 y = 96 t - 9 .8 t^{2} m$ . The angle of the projection is

Moderate

A

$\sin^{- 1} (\frac{4}{5})$
B

$\sin^{- 1} (\frac{3}{5})$
C

$\sin^{- 1} (\frac{4}{3})$
D

$\sin^{- 1} (\frac{3}{4})$

Solution

Given : $x = 36 t, 2 y = 96 t - 9 .8 t^{2}$ or $y = 48 t - 4 .9 t^{2}$
Let the initial velocity of projectile be u and angle of projection is $θ$ . Then,
Initial horizontal component of velocity,
$u_{x} = ucos θ = {(\frac{dx}{dt})}_{t = 0} = 36 or u \cos θ = 36 . . . . (i)$
Initial vertical component of velocity,
$u_{y} = usin θ = {(\frac{dy}{dt})}_{t = 0} = 48 or u \sin θ = 48$ …..(ii)
Dividing (ii) by (i), we get
$\tan θ = \frac{48}{36} = \frac{4}{3}; ∴ \sin θ = \frac{4}{5} or θ = \sin^{- 1} (\frac{4}{5})$

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