First slide

Projectile motion

Question

A ball is projected from the origin. The x- and y-coordinates of its displacement are given by $x = 3 t and y = 4 t - 5 t^{2}$ . Find the velocity of projection (in ${ms}^{- 1}$ ).

Moderate

Solution

$v_{x} = \frac{dx}{dt} = 3 and v_{y} = \frac{dy}{dt} = 4 - 10 t = 4 - 10 (0) = 4$
$v = {[v_{x}^{2} + v_{y}^{2}]}^{1 / 2} = {[3^{2} + 4^{2}]}^{1 / 2} = 5 {ms}^{- 1}$

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