First slide

Projectile motion

Question

A ball is projected from the ground at angle $θ$ with the horizontal. After 1 s, it is moving at angle 45^o with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?

Difficult

A

$10 \sqrt{3} {ms}^{- 1}$
B

$20 \sqrt{3} {ms}^{- 1}$
C

$10 \sqrt{5} {ms}^{- 1}$
D

$20 \sqrt{2} {ms}^{- 1}$

Solution

Suppose the angle made by the instantaneous velocity with the horizontal be $α$ . Then
$\tan α = \frac{v_{y}}{v_{x}} = \frac{u \sin θ - g t}{u \cos θ}$
$Given that α = 45^{\circ}, when t = 1 s; α = 0^{\circ}, when t = 2 s$
$This gives u \cos θ = u \sin θ - g . . . . (i)$
$and u \sin θ - 2 g = 0 . . . . . (i i)$
$Solving Eqs. (i) and (ii), we find u \sin θ = 2 g and u \cos θ = g .$
Squaring and adding,
$u = \sqrt{5} g = 10 \sqrt{5} {ms}^{- 1}$

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