Question

Consider the following statements A and B and mark the correct option.
A) The speed of the oblique projectile is minimum at the top of the path.
B) In case of a projectile motion, if the range $R$ is $n$ times the maximum height H then the angle of projection $\theta$ is equal to $ta{n}^{-1}\left(\frac{4}{n}\right)$

• A. Both A and B are true
• B. A is true but B is false
• C. B is true but A is false
• D. Both A and B are false

Answer 1

Answer: (A)

Both A and B are true

Statement A: In oblique particle projectile At any time,

$V_x=V\cos \theta$
$V_y=V\sin \theta -gt$
At top, $V_y=0,$ then it changes direction.
$V_x$ is constant. $\Rightarrow$ velocity is minimum at B.

Statement B:Range and maximum height in a oblique projectile are given as :

$R=\frac{V^2\sin 2\theta }{g},H_{max}=\frac{V^2{\sin }^2\theta }{2g}$
$R=n{H}_{max}\Rightarrow \frac{V^2}{g}\sin 2\theta =n\frac{V^2{\sin }^2\theta }{2g}\Rightarrow \tan \theta =\frac{4}{n}$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{4}{n}\right)$