-4.9t^2+100=-340t+780

Question

I am having problems solving this question. The original question is, A bungee jumper jumps from a bridge 100 meters above a gorge. Before the 40-meter-long rope begins to slow him down, his height is characterized by h(t)=-4.9t^2 +100. two seconds after he jumps, a car on the bridge blows out a tire. The sound of the tire blow-out moves down from the top of the bridge at the speed of sound and has a height given by h(t)=-340(t-2)+100. How high will the bungee jumper be when he hears the sound of the blowout?

Answer 1

In order for the jumper to hear the sound of the blowout, he needs to be at the same position of the sound.  So you have the correct equation.  Move all terms to the left side to get a quadratic equation.

 

-4.9t² + 340t - 680 = 0

 

 

Use the quadratic formula to solve for t.  Select the positive value of t, since time can only be positive.  Then evaluate any of the functions at that t value to get your height.