Question

A body is projected at time t = 0 with a velocity u at an angle $\theta$ with the horizontal. The horizontal and vertical components of its velocity will become equal at a time t $(t\ne 0)$ if,

• A. If $0\le \theta \le \frac{\pi }{4}$
• B. If $\frac{\pi }{4}\le \theta \le \frac{\pi }{2}$
• C. If $0\le \le \theta \le \frac{\pi }{6}$
• D. for no value of $\theta$

Answer 1

The correct option is B

If $\frac{\pi }{4}\le \theta \le \frac{\pi }{2}$

Horizontal component of velocity at a time t is $v_x=ucos\theta$

Vertical component of velocity at that time t is $v_y=usin\theta -gt$

They will become equal at time t if $ucos\theta =usin\theta -gt$

Which gives $t=\frac{u(sin\theta -cos\theta )}{g}$

Now t must be positive. Hence $sin\theta >cos\theta or\theta >\pi /4.$