Question

Genius question: A long level railway bridge passes over a railroad track, which is 100 feet below it and at right angles to it. If a law-abiding calculus student, one who always travels at the posted speed and who always does his homework, is traveling 45 miles per hour is directly above a train going 60 miles per hour below, how fast will they be separating 10 seconds later

Answer 1

Answer: 110 feet per second

Step-by-step explanation:

In this problem we will assume that the car at 45 miles per hour is moving into the x direction with a high of 100 feet, and the train is going in the y direction, so they trajectories will made an angle of 90º.

Now we can calculate the speed of the trains in feet per second so:

$S1=\frac{45*5280}{3600}=66$

$S2=\frac{60*5280}{3600}=88$

So we can make a right triangle with sides 66 and 88 and the hypotenuse will be the rate that the trains will separate per second so:

$h=\sqrt{66^{2} +88^{2} } =\sqrt{4356+7744}$

$h=\sqrt{12100}=110$

Is important to have in mind that the initial high is not going to change how fast the trains will separate, however, if we are going to calculate the distance we should have it in the calculations.