Question

Two particles start simultaneously from the same point and move along two straight lines making an angle $\alpha$ with each other. One move with uniform velocity u and the other with constant acceleration a and initial velocity zero. Then:

• A. The least relative velocity of one with respect to other is u sin $\alpha$.
• B. The least relative velocity of one with respect to other is u cos$\alpha$.
• C. When they have least relative velocity w.r.t. each other, distance between them is $\frac{u^{2}cos\alpha }{2a}\sqrt{1+3si{n}^2\alpha }.$
• D. Path followed by one as seen from other is parabolic.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The least relative velocity of one with respect to other is u sin $\alpha$.
C When they have least relative velocity w.r.t. each other, distance between them is $\frac{u^{2}cos\alpha }{2a}\sqrt{1+3si{n}^2\alpha }.$
D Path followed by one as seen from other is parabolic.


As seen from B, A particle is moving as shown in diagram below

$u_1=uand{u}_y=0a_x=-acos\alpha and{a}_y=-asin\alpha v_x=u-atcos\alpha v_y=-atsin\alpha v=\sqrt{v_x^2+v_y^2}$
For minimum value of v
$\frac{dv}{dt}=0$
By solving, we get
$t=\frac{ucos\alpha }{a}andv=usin\alpha x=ut-\frac{1}{2}a{t}^{2}cos\alpha y=-\frac{1}{2}a{t}^{2}sin\alpha distance,S=\sqrt{x^2+y^2}=\frac{u^{2}cos\alpha }{2a}\sqrt{1+3si{n}^2\alpha }$