Question

A particle P is projected with velocity $u_1$ at an angle of ${30}^{\circ }$ with the horizontal. Another particle Q is thrown vertically upwards with velocity $u_2$ from a point vertically below the highest point of path of P. The necessary condition for the two particles to collide at the highest point is

• A. $u_1=u_2$
• B. $u_1=2u_2$
• C. $u_1=\frac{u_2}{2}$
• D. $u_1=4u_2$

Answer 1

The correct option is B

$u_1=2u_2$

Both particle collide at the highest point it means the vertical distance travelled by both the particle will be equal, i.e. the vertical component of velocity of both particle will be equal

$u_{1}sin{30}^{\circ }=u_2\Rightarrow \frac{u_1}{2}=u_2\therefore u_1=2u_2$