- #1

Adesh

- 735

- 191

- Homework Statement
- Point A moves uniformly with velocity v so that the vector v is continually "aimed" at point B which in its turn moves rectilinearly and uniformly with velocity u<v. At the initial moment of time v is perpendicular to u and the points are separated by a distance l. How soon will the points converge ?

- Relevant Equations
- distance = integral of velocity with time.

The statement "

As the time passes velocity vector

$$\int_{0}^{t} v cosθ dt $$ = ut

$$\int_{0}^{t} v sinθ dt $$ = l

Now, here I'm stuck. I know that θ is a function of time but I can't figure out which function is it. I know that x-component of

*at the initial moment of time v ⊥ u and the points are separated by a distance l***"**gives us a picture like the one which I have added in attachment.As the time passes velocity vector

**v**would gradually change from fully vertical to fully horizontal in order to meet point B. Now, at any instant of time we have x-component of**v**as v cosθ and y-component as v sinθ. To catch point B our point A has to travel a distance of l in y- direction and to catch it in x-direction it has to cover the same distance as point B has covered. So, let's assume that they meet at time t , then$$\int_{0}^{t} v cosθ dt $$ = ut

$$\int_{0}^{t} v sinθ dt $$ = l

Now, here I'm stuck. I know that θ is a function of time but I can't figure out which function is it. I know that x-component of

**v**is gradually increasing sinusoidally and y-component is decaying sinusoidally but I'm not able to solve after that. I want to how can I solve for t after I have got those two equations.