First slide

Projection Under uniform Acceleration

Question

A small object is projected horizontally from the top of a tower of height 40 m with a velocity of 10 m/s. Simultaneously another small object is projected from the base of the tower with a velocity of 20 m/s making an angle $θ$ with horizontal in the same plane. If the objects collide at a point at time t, find t.

Difficult

Solution

$\begin{array}{l} h_{1} + h_{2} = 40 \\ \frac{1}{2} g t^{2} + u \sin θ . t - \frac{1}{2} g t^{2} = H \\ \Rightarrow t = \frac{H}{u \sin θ} = \frac{40}{20 \sin θ} = \frac{2}{\sin θ} \\ A g a i n, 10 \times t = 20 \cos θ \times t \Rightarrow θ = 60^{0} \\ ∴ t = \frac{2}{\sin 60^{0}} = \frac{4}{\sqrt{3}} \sec \end{array}$

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