Is there simpler way to approach this particle collision problem?

[joturttle]

Homework Statement

I do not know what this means

Relevant Equations

1/2AT^2
VT
D?

I was able to solve the problem, but my solution feels lengthy so i was curious if there was a mathematicallly simplier way to approach this problem.

 

[A.T.]

I was able to solve the problem, but my solution feels lengthy so i was curious if there was a mathematicallly simplier way to approach this problem.

Not sure if it's shorter or simpler, but it avoids trigonometric functions until the very end:

- Use Pythagoras to get the time to impact $t$
- Use $t$ to get the horizontal distance $s_x$
- Use $atan$ to get $\theta$

 

[Ibix]

Not sure if it's shorter or simpler, but it avoids trigonometric functions until the very end:

- Use Pythagoras to get the time to impact $t$
- Use $t$ to get the horizontal distance $s_x$
- Use $atan$ to get $\theta$

This would be my first guess too. Note that Pythagoras yields a quadratic in $t^2$, so I think finding the hypotenuse and using $\cos^{-1}$ is slightly shorter.