At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 pm?
2006-10-25 14:38:40 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Put A on origin at noon:
A = (0,0)
B east of A: (150,0)
Now the locations are a function of time:
A(t) = (35t,0),
B(t) = (150, 25t)
Now write equation for distance between A and B and differentiiate w.r.t. time:
D(t) = sqrt(A^2+B^2)
and evaluate at t=4
Get it?
2006-10-25 14:46:58 · answer #1 · answered by modulo_function 7 · 2⤊ 0⤋
Not quite sure how fast the distance is changing... I do know that at 4 o'clock the current distance between the two ships is approximately 100.498756211... It started at 150... So it decreased about 49.5013 km, which, divided by 4, is an average of about 12.375325 km/h... I don't know what else to do, sorry! So it doesn't ask what the current distance is? Weird.
2006-10-25 21:48:18 · answer #2 · answered by Mysterious 2 · 1⤊ 0⤋