Hot-air balloon problem

[gio]

Hi everyone,

I hope you can help me with the following problem.



A hot-air balloon, headed due east at an average speed of 15mph and at a constant altitude of 100 feet, passes over an intersection. Find an expression for the distance D (measured in feet) from the balloon to the intersection T seconds later.

 

[o_O]

Draw a diagram.

          D1
       __________
      |         /
      |        /
      |       /
      |      /
100   |     /    D2
      |    /
      |   /
      |  /
      | /
      |/
      *

You know that the airplane is 100 feet up and you know how fast he's travelling in the horizontal direction. So you can use the formula d = vt to figure out how far he has travelled in T seconds (D[sub:70xzxe0t]1[/sub:70xzxe0t]). Then, you just use Pythagoras' Theorem to find D[sub:70xzxe0t]2[/sub:70xzxe0t] to express the distance between the airplane and the intersection in terms of T.