AP Physics Question

Question

Ted is sitting in his lawn chair when Stella flies directly overhead, going southeast at 100 m/s. Five seconds later, a firecracker explodes 200 m east of Ted. What are the coordinates of the explosion in Stella's reference frame? Let Stella be at the origin, with her x-axis pointing to the east.

Answer 1

Well suppose Ted is at the origin.

If 1 unit is 1 m, then when the firecracker explodes it explodes at (200,0).

At time zero, Stella is at (0,0).

Her velocity is 100m/s southeast, so if vx and vy are her speeds east and south, then vx² + vy² = 100 and vx and vy are the same as the direction is southeast.

So 2 vx² = 100, so vx = √50, and vy is the same.

So after 5 seconds Stella is at (5 √ 50, -5√50) and the firecracker is at (200,0).

For Stella to be at (0,0) we need to move her position 5√50 to the left, and 5√50 up.

So we do the same to the firecracker position giving ( 200 - 5√50, 5√50).

This is the firecracker position in Stella's frame of reference.