First slide

Relative motion in 2 dimension

Question

A body is projected at an angle 30° with the horizontal with velocity v₁, from the point A. At the same time, another body is projected vertically upwards from B with velocity v₂.The point B lies vertically below the highest point of the trajectory of body projected from point A. For both the bodies to collide, the value of $\frac{v_{1}}{v_{2}}$ should be___ .

Moderate

Solution

The two bodies will collide at the highest point if both cover the same vertical height in the same time. So
$\frac{v_{1}^{2} \sin^{2} 30^{\circ}}{2 g} = \frac{v_{2}^{2}}{2 g}$ or
$\frac{v_{2}}{v_{1}} = \sin 30^{\circ} = \frac{1}{2} ∴ \frac{v_{1}}{v_{2}} = 2$

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