Assignment:
Suzy Sorority agrees to give Joe Student a ride home for spring break. They agree to meet at the corner of 12thst. and Willow. Joe is late and Suzy gets tired of waiting, so she starts to drive off down Willow st. without him. Joe was already walking down 12thst., and he starts to shout and run towards the corner when he sees the car pull away. Assume that Willow and 12thst streets are perfectly perpendicular.
a) Let x(t) denote the distance between Joe and the corner at time t, let y(t) denote Suzy's distance from the corner, and let z(t) denote the distance between Joe and Suzy. Find an equation which relates x, y, z,dx/ dt ,dy/dt and dx/dt.
b) At a certain moment, Suzy's car is 30 ft from the corner and it is moving at 12 ft/sec and Joe is 40 ft from the corner and he is running at 10 ft/sec Use your answer to (a) to find the rate of change of the distance between them at this moment. Are they getting closer or farther apart at this moment?
Provide complete and step by step solution for the question and show calculations and use formulas.