Worksheet 3.8 Related Rates - Calculus Maximus Page 3
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7Calculus Maximus
WS 3.8: Related Rates
6. (2002B AB6) Ship A is traveling due west toward
Lighthouse Rock at a speed of 15 kilometers per hour
(km/hr). Ship B is traveling due north away from
Lighthouse Rock at a speed of 10 km/hr. Let x be the
distance between Ship A and Lighthouse Rock at time
t, and let y be the distance between Ship B and
Lighthouse Rock at time t, as shown in the figure at
right.
(a) Find the distance, in kilometers, between Ship A
x km and
y km.
and Ship B when
4
3
x km and
(b) Find the rate of change, in km/hr, of the distance between the two ships when
4
y km.
3
(c) Let be the angle shown in the figure. Find the rate of change of , in radians per hour, when
x km and
y km.
4
3
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