Particle A moves along the line y = 30m with a constant velocity v og manitude 3.0m/s and parallel to .......?

Question

the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant accleration a of magnitude 0.40 m/s2. What angle θ between a and the positive direction of the y axis would result in a collision?

Answer 1

Write down the equations of motion for the two particles.
For A: x = 3t y=30
For B: x = a t^2 cos (th) y = a t^2 sin (th) where a is the acceleration.
Equate the x and y:
3 t = a t^2 cos (th) and 30 = a t^2 sin (th)
and solve for t and theta. This can be done quickest by 1) squaring and adding both equations 2) dividing both equations.
This leaves you with a quadratical equation in t^2, with solution t=10.4 seconds and tan (th) = 30/(3t) or theta = 43.9 degree.