Calculus

Two trucks start from the same point. One truck travels due east at a rate of 50 mph and the other trucks travels due north at a rate of 60 mph. At what rate is the distance between the two vehicles increasing 1 1/2 hours later?

I think the answer is 55 mph because I added 60 + 55 and divided by 2 and got 55 mph.

  1. 👍
  2. 👎
  3. 👁
  1. Oh my :(

    The distance between them is the hypotenuse of a right triangle.

    D^2 = x^2 + y^2
    where
    x = 50 t
    y = 60 t
    so
    D^2 = 2500 t^2 + 3600 t^2 = 6100 t^2
    now take time derivative

    2 D dD/dt = 12200 t
    at t = 1.5
    D^2 = 6100 (2.25)
    D = 117 miles
    2 D = 234.3 miles
    so
    dD/dt = 12200(1.5)/234.3 = 78.1 miles/hour

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A truck travels due east for a distance of 1.7 km, turns around and goes due west for 7.1 km, and finally turns around again and travels 3.5 km due east. What is the total distance that the truck travels? What are the magnitude

  2. Physics

    Two bicyclists, starting at the same place, are riding toward the same campground by different routes. One cyclist rides 1030 m due east and then turns due north and travels another 1480 m before reaching the campground. The

  3. physics

    A 6000kg truck travelling north at 5m/s collides with a 4000kg truck moving west at 15m/s,if the two trucks remain locked together after collision,find (a)with what speed and in what direction do they move immediately after

  4. math

    A man travels 12km due north, then 5km due east and then back to the starting point on a straight road. What is the total distance traveled?

  1. Physics

    An ocean liner leaves New York City and travels 25.1 degrees north of east for 110km. How far east and how far north has it gone? In other words, what are the magnitudes of the components of the ships displacement vector in the

  2. calculus

    Two cars start from the same point at the same time. One travels north at 25 mph, and the other travels east at 60 mph. How fast is the distance between them increasing at the end of 1 hr? Find D after 1 Hr, solve D^2=25^2+ 60^2

  3. Geometry 1

    Ship A and Ship B leave from the same point in the ocean. Ship A travels 150 mi due west, turns 65° toward north, and then travels another 100 mi. Ship B travels 150 mi due east, turns 70° toward south, and then travels another

  4. math

    Two trucks left buck's trucks traveling in opposite directions. One truck traveled at a rate of 70km/h, the other at 80km/h. After how many hours were the trucks 900km apart? I got 3 hours as my answer, but I don't think that's

  1. Precalc 2

    At a state fair truck pull, two pickup trucks are attached to the back end of a monster truck as illustrated in the figure. One of the pickups pulls with a force of 1600 pounds and the other pulls with a force of 3200 pounds with

  2. Physics

    A truck moves 70m east, then moves 120m west, and finally moves east again a distance of 90 m. If east is chosen as the positive direction, what is the trucks resultant displacement?

  3. Science

    A truck is moving north at a speed of 70 km/h. The exhause pipe above the truck cab seeds out a tail of smoke that makes an angle of 20 degree east of south behind the truck. If the wind is flowing directly towards the east. What

  4. physics

    An engine of mass 5000 kg pulls a train of ten trucks each of mass 2000 kg along a horizontal track. Assume that the frictional forces to be 5000 N and that the engine exerts a force of 50 000 N on the rails. If the trucks are

You can view more similar questions or ask a new question.