Question

A particle is moving with velocity v = $100m{s}^{-1}$ . If one of the rectangular components of a velocity is $50m{s}^{-1}$. Find the other component of velocity and its angle with the given component of velocity.

• A. Magnitude $=100\sqrt{3}m{s}^{-1}$ Angle $={30}^{\circ }$
• B. Magnitude $=120\sqrt{3}m{s}^{-1}$ Angle $={40}^{\circ }$
• C. Magnitude $=50\sqrt{3}m{s}^{-1}$ Angle $={60}^{\circ }$
• D. Magnitude $=80\sqrt{3}m{s}^{-1}$ Angle $={30}^{\circ }$

Answer 1

The correct option is C

Magnitude $=50\sqrt{3}m{s}^{-1}$

Angle $={60}^{\circ }$

Here we are given net velocity $v=100m{s}^{-1}$
$Let{v}_x=50m{s}^{-1}\Rightarrow v_x=vcos\theta \Rightarrow 50=100cos\theta \Rightarrow cos\theta =\frac{1}{2}or\theta ={60}^{\circ }\therefore v_y=vsin\theta =100sin{60}^{\circ }=100\times \frac{\sqrt{3}}{2}=50\sqrt{3}m{s}^{-1}$