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About Scotto
Expertise
Any kind of mathematics (algebra, geometry, trigonometry, matrices, calculus, linear approximation, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics, Chemistry, and Biology. I would like to volunteer in all areas of Mathematics, not just calculus, and the other three courses that were mentioned.

Experience
Experience in the area: I have tutored students in all areas of mathematics for over 20 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
 
   

You are here:  Experts > Teens > Homework/Study Tips > Calculus > Calculus-Related Rates

Topic: Calculus



Expert: Scotto
Date: 7/15/2008
Subject: Calculus-Related Rates

Question
I tried to work on these problems but I'm not completely sure how to start it and if I was doing it right.

A car passes over a bridge at 15.0 m/s at the same time a boat passes under the bridge at a point 10.5m directly below car. If the boat is moving perpendicularly to the bridge at 4.0m/s, how fast are the car and the boat separating 5.0s later?

A weather balloon leaves the ground 275m from an observer and rises vertically at 12.0m/s. How fast is the line of sight from the observer to the balloon increasing when the balloon is 450m high?

Answer
The car is moving one way at 15 m/s and the boat is moving 4 m/s.
Multiply the speed by 5 seconds to get how far they have gone.
Let c = car distance, b = boat distance, k = diagonal.

The equation would be b^2 + c^2 = k^2.  Take the derivative with respect to t with b, c, and k all functions of t.  The variables b and c were calculated, and then k can be found.  db/dt and dc/dt were given.  The equatioin is 2b(db/dt) + 2c(dc/dt) = 2k(dk/dt).  Solve for dd/dt.

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