Motion in a Plane - Result Question 36
39. Two projectiles are fired from the same point with the same speed at angles of projection $60^{\circ}$ and $30^{\circ}$ respectively. Which one of the following is true?
[2000] (a) Their maximum height will be same
(b) Their range will be same
(c) Their landing velocity will be same
(d) Their time of flight will be same
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Answer:
Correct Answer: 39. (b)
Solution:
- (b) Given, $u_1=u_2=u, \theta_1=60^{\circ}, \theta_2=30^{\circ}$
In $1^{\text{st }}$ case, we know that range
$R_1=\frac{u^{2} \sin 2(60^{\circ})}{g}=\frac{u^{2} \sin 120^{\circ}}{g}$
$ \begin{aligned} & =\frac{u^{2} \sin (90^{\circ}+30^{\circ})}{g} \\ & =\frac{u^{2}(\cos 30^{\circ})}{g}=\frac{\sqrt{3} u^{2}}{2 g} \end{aligned} $
In $2^{\text{nd }}$ case, when $\theta_2=30^{\circ}$, then
$ R_2=\frac{u^{2} \sin 60^{\circ}}{g}=\frac{u^{2} \sqrt{3}}{2 g} \Rightarrow R_1=R_2 $
[we get same value of ranges].
