1. ## Basic Differential Equation

A water balloon launched from the roof of a building at time t = 0 seconds has vertical velocity v(t) = -32t + 40 feet/sec with positive v corresponding to upward motion.

(a) If the roof of the building is 50 feet above the ground, find an expression for the height of the water balloon above the ground at time t.

40t-16t^2+50

(b) What is the average velocity of the water balloon between t = 1 and t = 2 seconds?

-8

(c) A 6-foot person is standing on the ground. How fast is the water balloon falling when it strikes the person on the top of the head? Give an exact value.

I got -8*sqrt(69) for (c) but am not sure if that is the right answer.

2. You got it right.

3. Originally Posted by Latszer
A water balloon launched from the roof of a building at time t = 0 seconds has vertical velocity v(t) = -32t + 40 feet/sec with positive v corresponding to upward motion.

(a) If the roof of the building is 50 feet above the ground, find an expression for the height of the water balloon above the ground at time t.

h(t) = 40t-16t^2+50

(b) What is the average velocity of the water balloon between t = 1 and t = 2 seconds?

-8 ft/s ... correct

(c) A 6-foot person is standing on the ground. How fast is the water balloon falling when it strikes the person on the top of the head? Give an exact value.

I got -8*sqrt(69) ft/s for (c) but am not sure if that is the right answer.

that is correct if the question asks for the velocity ... speed would be the absolute value of that quantity.
...

4. I looked at it and it said speed, so thanks you two.