How High and At What Angle Should Person B Shoot to Hit Person A?

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SUMMARY

The problem involves calculating the angle and height at which Person B must shoot an arrow to hit Person A, who is launched from a cannon at 100 m/s at a 30-degree angle from a 75-meter cliff. The equations governing the motion of both individuals include projectile motion formulas, specifically for Person A's trajectory and Person B's arrow. The key equations are X_Ay and X_Ax for Person A's position and X_By for Person B's position, with the need to isolate the angle θ for the arrow's launch. The solution requires equating the coordinates of both projectiles at the time of impact.

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Homework Statement


Person A is shot out of cannon at 100m/s at 30 degrees above the horizontal on top of a 75 meter tall cliff. After 3 seconds, Person B, standing next to the cannon, shoots an arrow at 200m/s at Person A. At what height does the arrow strike person A, and what angle did he fire at?

Homework Equations


X_Ay=75+200 sin⁡(θ) (t-3)+g/2 〖(t-3)〗^2
X_Ax=200 cos⁡(θ) (t-3)
X_By=75+50t+g/2 t^2
X_By=86.6t

The Attempt at a Solution


{(75+200sin(θ)(t-3)+g/2(t-3)^2)^2 + (200cos(θ)(t-3))^2}^1/2 = {(75+50t+g/2 t^2)^2 + (86.6t)^2}^1/2

For some reason I am unable to isolate theta
 
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Make use of the fact that A and B must have the x and y coordinates when they collide.
 

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