Three particles start simultaneously from a p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the starting point be the origin $(0, 0)$.After time $t$,the position of the first particle is $(v_1 t, 0)$ and the second particle is $(0, v_

Vedclass · Accepted Answer

$\sqrt{2} \frac{v_1 v_2}{v_1+v_2}$

Vedclass · Answer

(D) Let the starting point be the origin $(0, 0)$.After time $t$,the position of the first particle is $(v_1 t, 0)$ and the second particle is $(0, v_2 t)$.The equation of the line passing through these two points is $\frac{x}{v_1 t} + \frac{y}{v_2 t} = 1$,which simplifies to $v_2 x + v_1 y = v_1 v_2 t$.The third particle moves towards the north-east,meaning its velocity vector makes an angle of $45^\circ$ with the x-axis. Its position at time $t$ is $(v_3 t \cos 45^\circ, v_3 t \sin 45^\circ) = (\frac{v_3 t}{\sqrt{2}}, \frac{v_3 t}{\sqrt{2}})$.Since the third particle must lie on the same line,substitute its coordinates into the line equation:$v_2 (\frac{v_3 t}{\sqrt{2}}) + v_1 (\frac{v_3 t}{\sqrt{2}}) = v_1 v_2 t$.Dividing by $t$ and solving for $v_3$:$\frac{v_3}{\sqrt{2}} (v_1 + v_2) = v_1 v_2$.$v_3 = \frac{\sqrt{2} v_1 v_2}{v_1 + v_2}$.

Similar Questions

If a body moving in a circular path maintains a constant speed of $10\,ms^{-1},$ then which of the following correctly describes the relation between acceleration and radius?

An object is projected with kinetic energy $K$ from a point $A$ at an angle $60^{\circ}$ with the horizontal. In the absence of air friction, what is the ratio of the difference in kinetic energies at points $B$ and $C$ to the kinetic energy at point $A$ (see figure)?

$A$ particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is ($g=$ acceleration due to gravity).

$A$ body of mass $m$ is projected at an angle of $45^{\circ}$ with the horizontal with an initial velocity $v$. If air resistance is negligible,then the total change in momentum when it strikes the ground is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module