Homework Help: Calculus

Posted by Jo on Tuesday, October 25, 2011 at 12:10am.

A balloon is rising vertically above a level, straight road at a constant rate of 1 foot/second. Just when the balloon is 65 feet above the ground, a bicycle passes under it going 17 feet/sec. How fast is the distance between the bicycle and balloon increasing 3 seconds later?

Calculus - Reiny, Tuesday, October 25, 2011 at 8:37am
let the time passed since the biker passed directly underneath be t seconds
Make a diagram showing the distance between them as d ft
I see it as
d^2 = (17t)^2 + (65+t)^2
when t=3
d^2 = 51^2 + 68^2
d = √7225 = 85

2d dd/dt = 2(17)(17t) + 2(65+t)
divide by 2 and solve for dd/dt
dd/dt = (17(17t) + 65+t)/d
when t=3 and d = 85
dd/dt = (17(51) + 68)/85 = 11 ft/s

Answer this Question

Related Questions

Calculus - A hot-air balloon is 180 ft above the ground when a motorcycle ...
calculus - A hot-air balloon is 150 feet above the ground when a motorcycle ...
Hot-air balloon - A hot-air balloon is 180 ft above the ground when a motorcycle...
Math - a balloon is rising vertically at the rate of 2 m/s. an observer is ...
calculus - A hot air balloon rising straight up form a level field is tracked by...
Math - A hot air balloon is rising vertically. From a point on level ground 125 ...
Calculus - A hot air balloon rising vertically is tracked by an observer located...
Pre-Calc - A hot-air balloon is floating above a straight road. To estimate ...
physics - A hot air balloon has just lifted off and is rising at the constant ...
Physics - A balloonist, riding in the basket of a hot air balloon that is rising...

For Further Reading

First Name:
School Subject:
Answer: