h=-4.9t^2+23.8t+3.5

Question

A toy rocket is launched from a 3.5 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h=-4.9t^2+23.8t+3.5. How long will it take for the rocket to hit the ground? (answer in seconds)

Answer 1

When the rocket hits the ground, the height, h, will equal 0. So set your equation equal to zero and solve using the quadratic equation.

h=-4.9t² + 23.8t + 3.5

0 = -4.9t² + 23.8t + 3.5

 

Using the quadratic equation, t=-0.1428 and t=5. Since a negative value for time doesn't make sense for this problem, we will discard it and go with 5 seconds.

 

So, the rocket will hit the ground 5 seconds after it is shot into the air.

 

Hope this helps,

Chris