Question:
Two particles start simultaneously from the same point and move along two straight line . One with uniform Velocity v and other with a uniform acceleration a. If $\alpha$ is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by
Two particles start simultaneously from the same point and move along two straight line . One with uniform Velocity v and other with a uniform acceleration a. If $\alpha$ is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by
Updated On: Jul 7, 2022
- $\frac{v}{a}\sin \,\alpha$
- $\frac{v}{a}\cos \,\alpha$
- $\frac{v}{a}\tan \,\alpha$
- $\frac{v}{a}\cot \,\alpha$
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The Correct Option is B
Solution and Explanation
$\nu_r$ is subtraction of vectors. Hence,
$\nu^2_r$ = x(say) = $\nu^2 + (at)^2 $ - 2v (at) cos $\alpha$
Now , $\nu_r$ will be minimum when x is minimum
Hence $\frac{dx}{dt} $ = 0 or $2a^2 t - 2\nu a$ cos $\alpha$ = 0
t = $\frac{\nu \, \cos \, \alpha}{a}$
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Concepts Used:
Relative Velocity
The velocity with which one object moves with respect to another object is the relative velocity of an object with respect to another. By relative velocity, we can further understand the time rate of change in the relative position of one object with respect to another.
It is generally used to describe the motion of moving boats through water, airplanes in the wind, etc. According to the person as an observer inside the object, we can compute the velocity very easily.
The velocity of the body A – the velocity of the body B = The relative velocity of A with respect to B
V_{AB} = V_{A} – V_{B}
Where,
The relative velocity of the body A with respect to the body B = V_{AB}
The velocity of the body A = V_{A}
The velocity of body B = V_{B}