Question

A yellow hot-air balloon is 100 feet off the ground and rising at rate of 8 feet per second.An orange hot-air balloon is 160 feet off the ground and rising at a rate of 5 feet per second. After how long will the Yellow balloon be higher than the orange balloon?

Answer 1

Find out the how long will the Yellow balloon be higher than the orange balloon.

To proof

Now the diagram is given below

As given

A yellow hot-air balloon is 100 feet off the ground and rising at rate of 8 feet per second.

i.e height of the yellow baloon off the ground = 100 feet

rising at rate = 8 feet per second.

.An orange hot-air balloon is 160 feet off the ground and rising at a rate of 5 feet per second.

i.e height of the orange baloon off the ground = 160 feet

rising at rate = 5feet per second.

Formula

`Relative\ velocity = (Relative\ Distance)/(Relative\ time)`

Relative velocity = rising rate of yellow balloon - rising rate of orange balloon

= 8 -5

= 3 feet per second

Relative distance = height of the yellow baloon off the ground - height of the orange baloon off the ground

= 160 -100

= 60 feet

put in the formula

`= (60)/(3)`

= 20 second

after 20 second Yellow balloon will be higher than the orange balloon.

Hence proved