November 9th, 2017, 01:43 PM  #1 
Newbie Joined: Nov 2017 From: Canada Posts: 4 Thanks: 0  Related rates  bridge / boat
A bridge goes across the river at a height of 60m. A car on the bridge travelling at 40 m/s passes directly over a boat travelling up the river at 15 m/s. Find the rate at which the distance between the car and the boat is increasing 3 seconds later?

November 10th, 2017, 03:24 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,242 Thanks: 885 
One method: set up a coordinate system so that (0, 0, 0) is the position of the boat directly under the bridge and (0, 0, 60) is the position of the car with the xaxis parallel to the bridge. What are the positions of the boat and car t seconds later? What is the distance between those two points? Differentiate that formula with respect to t to find the rate of change of that distance.


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