Calvin and Phoebe elope in a hot air balloon, which rises at a constant rate of 3 meters per second. Five seconds after they cast off, Phoebe's jilted suitor Bonzo McTavish races up in his Porsche. He parks 50 meters from the launch pad, and runs toward the pad at 2 meters per second. At what rate is the distance between Bonzo and the balloon changing when the balloon is 30 meters above the ground?

Question

jamesj · Answer

Step 1: draw a diagram
Step 2: figure out a formula as a function of time for
           - the position of Bonzo 
           - the position of the balloon
Step 3: Now write down a function of time for the distance between Bonzo and the balloon (Pythagorus Theorem)
Step 5: Find the time t and which the height of the balloon is 30 meters
Step 4: Differentiate that function and evaluate the derivative at the time at which the balloon is at 30 meters