First slide

Projection Under uniform Acceleration

Question

A body is projected with a velocity 60 ms^-1 at 30⁰ to horizontal. The displacement after 2 s is

Moderate

A

$\large (30\sqrt{3}\hat i+30 \hat j)m$
B

$(60\sqrt{3}\hat i+40 \hat j)m$
C

$(10\sqrt{3}\hat i+10 \hat j)m$
D

$(40\sqrt{3}\hat j+40 \hat i)m$

Solution

$\overline S = {S_x}\widehat i + {S_y}\widehat j = (u\cos \theta )t\widehat i + \left( {u\sin \theta t - \frac{1}{2}g{t^2}} \right)\widehat j$
$= 30\sqrt 3 \times 2\widehat i + \left( {30 \times 2 - \frac{1}{2} \times 10 \times 4} \right)\widehat j$
$= (60\sqrt 3 \widehat i + 40\widehat j)\;m$

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