Answer to Question #330615 in Calculus for Gaile

Question

A boy in a hot air balloon drops his cellular phone when the balloon is 150 ft above the ground and rising at the rate of 10 ft/s.

a.How long will it take the cellular phone to reach the ground?

b. With what speed will it strike the ground?

Answer 1

a. $h(t)=150+10t-16t^2.$

$h(t)=0 \to 150+10t-16t^2=0 \to t=\frac{5+\sqrt{25+9600}}{32}=3.39 s.$

The cellular reaches the ground in 3.39 seconds.

b. $v(t)=10-32t.$

$v(3.39)=10-32*3.39=-98.48ft/s.$