Question

A truck is moving horizontally with velocity $v$. A ball thrown vertically upward with a velocity $u$ at angle $\theta$ to the horizontal from the truck relative to it. The horizontal range of the ball relative to the ground is

• A. $\frac{2\times (v+u\cos \theta )u\sin \theta }{g}$
• B. $\frac{2\times (v+u\sin \theta )u\cos \theta }{g}$
• C. $\frac{2\times (v-u\cos \theta )u\sin \theta }{g}$
• D. $\frac{2\times (v-u\sin \theta )u\cos \theta }{g}$

Answer 1

The correct option is A $\frac{2\times (v+u\cos \theta )u\sin \theta }{g}$

Velocity of truck=v

velocity of truck =u

At an angle $\theta$ ,time of flight:

$u_y=u_y-gt$

$0=u_y-g\frac{T}{2}$

$T=\frac{2u_y}{g}=\frac{2u\sin \theta }{g}$

Range=$(u_x+v)\times T=(v+u\cos \theta )\times \frac{2u\sin \theta }{g}$