I know that the starting point is (-50,0) but I'm not sure what to do after that! Thanks!

Question

Jeremy's coach makes him run clockwise around a circular track with radius of 50 meters. Jeremy manages to maintain a constant speed around the track. He takes 48 seconds to finish one lap of the track. From his starting point, it takes him 12 seconds to reach the northernmost point of the track. Answer the following questions below assuming that the center of the track at the origin and the northernmost point is on the y-axis.

Give Jeremy's coordinates at his starting point.

Give Jeremy's coordinates when he has been running for 4 seconds.

Give Jeremy's coordinates when he has been running for 32 seconds.

Answer 1

DRAW A PICTURE !!

Using N-E-S-W (clockwise) directions, we have:

W: (0 sec) point W(-50,0) [note: radius is 50]

N: (12 sec) point N(0,50) [note: radius is 50]

[note: constant speed; (48 sec per lap), so (12 sec per quarter)]

E: (24 sec) point E(50,0) [radius 50; 12 more sec]

S: (36 sec) point S(0,-50) [radius 50; 12 more sec]

W: (48 sec) point W(-50,0) [one lap completed]

Give Jeremy's coordinates at his starting point. [-50,0]

Give Jeremy's coordinates when he has been running for 4 seconds. [note: WestNorthWest]

He had moved from 9 o.clock to 10 o'clock. This forms a 1n, n√3, 2n triangle with 2n=50,

so n=25 and the triangle is 25, 25√3, 50

Point is ( -25√3, 25 )

Give Jeremy's coordinates when he has been running for 32 seconds.

He is now 4 seconds short of South (6 o'clock). [note:SouthSouthEast]

See calculations above: this is also a 1n, n√3, 2n triangle with n=25.

Point is ( 25. -25√3 )