Question

Two stories A and B are projected with the same velocity at angles of projection $20$ and $70$ repectively. If H and H be the horizontal ranges, then:

• A. $0.697$
• B. $0.764$
• C. $0.642$
• D. $0.564$

Answer 1

Answer: (C)

$0.642$

We know range of a projectile,$R=\frac{v_0^2\sin 2\theta }{2g}$

Now horizontal range of the projectile A,$R_A$ when $\theta ={20}^0$

$R_A=\frac{v_0^2\sin 40}{2g}⟹\left(1\right)$ and

$R_B=\frac{v_0^2\sin 140}{2g}⟹\left(2\right)$ here both A and B possess same velocity.

Now dividing equations (2) and (1) we get ratio of horizontal ranges

$R_B{R}_A=\frac{{v_0}^{2}sin140}{2g}\times \frac{{v_0}^{2}sin40}{2g}=0.6427$