Question

A particle P is projected with velocity u₁ at an angle of 30^o with the horizontal. Another particle Q is thrown vertically upwards with velocity u₂ 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

Answer: (B)

$u_{1} = 2u_{2}$

Answer 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

$u_{1}\sin 30{^\circ} = u_{2}$ ⇒ $\frac{u_{1}}{2} = u_{2}$ ∴ $u_{1} = 2u_{2}$