First slide

Projection Under uniform Acceleration

Question

A particle A is projected from the ground with an initial velocity of 10 m/s at an angle of 60^o with horizontal as shown in fig. (4). From what height h
should an another particle B be projected horizontally with velocity 5 m/s so that both the particles collide in ground at point C if both are projected simultaneously ?(g = 10 m/s²)

Moderate

A

10 m
B

30 m
C

15 m
D

25 m

Solution

The horizontal component of velocity is given by
$ucos θ = 10 \times \cos 60^{\circ} = 10 \times (1 / 2) = 5 m / s$
This is same as the velocity of B in horizontal direction. Both wilt collide at C if their times of flights are equal, i.e., T_A = T_B
$\frac{2 usin θ}{g} = \sqrt{(\frac{2 h}{g})} (∵ h = \frac{1}{2} {gT}_{B}^{2})$
$∴ h^{2} = \frac{2 u^{2} \sin^{2} θ}{g} = \frac{2 \times (10)^{2} (\sqrt{3} / 2)^{2}}{10} = 15 m$

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