What is the Speed of the Truck?Date: 20 Mar 1995 20:28:17 -0500 From: Anonymous Subject: A hard math problem Dear Dr. Math, I have a math problem for you. See if you can solve it. 1. A storm is 50 miles offshore and its path is perpendicular to a straight shoreline. It is approaching the shore at a rate of 4mph. A van traveling along the shore wants to stay exactly 50 miles from the storm and remain on the shoreline. The van starts at the point on the shoreline in the path of the storm. a. Determine a formula for the speed that the truck must maintain to remain 50 miles from the storm. b. Find the speed of the truck when the storm is 40 miles from the shore. Please reply if you can. Thanks so much. Sincerely, Chad Martin Date: 21 Mar 1995 21:50:01 -0500 From: Dr. Ken Subject: Re: A hard math problem Hello there! Here's how I would tackle this problem. Label the van by the letter, V, the van's starting point by the letter, B, and the storm by the letter, S. Then we know that the triangle VBS is a right triangle. Now label the sides opposite V, B, and S by the small letters v, b, and s. Then we know that b=50, and so v^2 + s^2 = 2500. Now find an equation for the distance the storm is away from the shore (in terms of time), and plug that into the above formula, substituting for v. Then you should be able to solve for v. That will give you the DISTANCE the van has to go as a function of time. Do you know how to find the velocity function when you have the distance function (think Calculus)? Hope this helps. Write back if you're still confused. -Ken "Dr." Math |
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