Quiz (Rates of Change)

Show all work and justify each step. Write answers in complete sentences.

(1) If an arrow is shot upward on the moon with a velocity of its height in meters after seconds is given by

    (a) Find the velocity of the arrow after
    
    (b) Find the velocity of the arrow when
    
    (c) When will the arrow hit the moon?
    
    (d) With what velocity will the arrow hit the moon?

(2) If a cylindrical tank holds gallons of water, which takes to drain from the bottom of the tank, then Torricelli's Law given the volume of water remaining in the tank after minutes as



Find the rate at which the water is flowing out of the tank after 20 minutes.

(3) A ball is thrown straight down from the top of a 220-foot building with an initial velocity of 120 meters per second. What is the velocity after 5 seconds? After 10 seconds?

(4) To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. How high is the building if the splash is seen seconds after the stone is dropped?  

(5) Verify that the average over the time interval is the same as the instantaneous velocity at for the position function

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