Question

The minimum and maximum velocity of an oblique projectile are $10m/s$ and $20m/s$ respectively. The maximum height is____________

• A. $20m$
• B. $15m$
• C. $30m$
• D. $10m$

Answer 1

The correct option is B $15m$

At the time t=0, the projectile has the maximum speed vertically. At the maximum height the projectile has minimum $\theta$ vertical speed.

$\varphi =$ angle of projection

So minimum speed $=u\cos \varphi =10m/s$

Maximum speed $=u=20m/s$

So $\cos \varphi =\frac{10}{20}=\frac{1}{2}\Rightarrow \varphi {60}^{\circ }$

Horizontal range $=R=\frac{u^2\sin 2\varphi }{g}=\frac{{20}^2\sin {120}^{\circ }}{10}$

$R=20\sqrt{3}m$

Maximum height $=H=\frac{u^2{\sin }^2\varphi }{2g}=\frac{{20}^2\times \frac{3}{4}}{2\times 10g}$

$H=15m$