Engineering Board Exam Reviewer · Related Rates (Time Rates) · hard

A balloon leaves the ground 500 ft from an observer and rises vertically at 140 ft/min. Find the rate at which the angle of elevation is increasing after 3 minutes (when the balloon is 420 ft high).

0.164 rad/min
0.28 rad/min
0.20 rad/min
0.140 rad/min

Answer

A. 0.164 rad/min

Solution

=h/500, so 2 /dt=1/500dh/dt=140/500=0.28. At h=420, the line-of-sight distance is sqrt(5002+4202) 653.0, giving 2 1.706. So d /dt 0.28/1.706 0.164 rad/min.

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