Question

A projectile is fired at an angle of 30⁰ to the horizontal such that the vertical component of its initial velocity is 80 $m s^{- 1}$ . Its time of flight is T. Its velocity at t = T/4 has a magnitude of nearly

Moderate

Solution

$\tan 30 ° = \frac{u_{y}}{u_{x}}$
$∴ \frac{1}{\sqrt{3}} = \frac{80}{u_{x}} or u_{x} = 80 \sqrt{3} {ms}^{- 1}$
$T = \frac{2 u_{y}}{g} = \frac{2 \times 80}{10} = 16 s$
At $t = \frac{T}{4} = 4 s \Rightarrow v_{x} = u_{x} = 80 \sqrt{3} {ms}^{- 1} and v_{y} = u_{y} + a_{y} t$
$or v_{y} = 80 + (- 10) (4) = 40 {ms}^{- 1}$
$∴$ Velocity $= \sqrt{(80 {\sqrt{3)}}^{2} + (40)^{2}} = 144.2 {ms}^{- 1}$

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