How Fast is the Distance Between a Rising Balloon and a Cycling Boy Increasing?

[venom_h]

Homework Statement

A balloon is rising at a constant speed of 5ft/s. A boy cycling along a straight road at a speed of 15 ft/s. When he passes directly under the balloon, it is 45 ft above him. how fast is the distance between the boy and the balloon increasing 3 seconds later?

Homework Equations

s^2= x^2+y^2
dx/dt = 15ft/s; dy/dt = 5ft/s

The Attempt at a Solution

2s(ds/dt)=2x(dx/dt)+2y(dy/dt)
Now, the problem is, how do i find the general equation for me to pluck in the t?

 

[HallsofIvy]

Homework Statement

A balloon is rising at a constant speed of 5ft/s. A boy cycling along a straight road at a speed of 15 ft/s. When he passes directly under the balloon, it is 45 ft above him. how fast is the distance between the boy and the balloon increasing 3 seconds later?

Homework Equations

s^2= x^2+y^2
dx/dt = 15ft/s; dy/dt = 5ft/s

The Attempt at a Solution

2s(ds/dt)=2x(dx/dt)+2y(dy/dt)
Now, the problem is, how do i find the general equation for me to pluck in the t?

What do you mean by "the general equation"? You've already used the most general equation here- s^2= x^2+ y^2. You have, correctly 2s(ds/dt)+ 2x(dx/dt)+ 2y(dy/dt) (you might divide through by 2 to simplify.) You know dx/dt= 15 ft/s, dy/dt= 5 ft/s and certainly should be able to find x and y "3 seconds later" (how far does the boy go in 3 sec.? How far does the balloon rise in 3 sec.? And you can calculate s at that time. That's all you need.