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

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AI Thread Summary
To determine the angle at which Person B should shoot to hit Person A, the equations of motion for both individuals are set up based on their respective velocities and heights. Person A is launched from a 75-meter cliff at 100 m/s at a 30-degree angle, while Person B shoots an arrow at 200 m/s after a 3-second delay. The key equations involve the vertical and horizontal positions of both persons over time, factoring in gravity. The challenge lies in isolating the angle theta for Person B's shot, ensuring that both x and y coordinates match at the point of collision. The solution requires careful manipulation of the equations to find the correct angle and height at which the arrow strikes Person A.
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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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