A rocket is propelled vertically upwards with an initial velocity of 20 meters per second. The distance, s, in meters, of the rocket from the ground after t seconds is given by : s = -4.9t (to the second power) + 20t. When will it strike the ground?

Question

A rocket is propelled vertically upwards with an initial velocity of 20 meters per second.  The distance, s, in meters, of the rocket from the ground after t seconds is given by : s = -4.9t (to the second power) + 20t.  When will it strike the ground?

anonymous · Answer

Well, s is the distance from the ground. When it strikes the ground, s = 0.

So, solve the equation:

$$0 = -4.9t^2 + 20t$$

anonymous · Answer

Note that you should get two answers: t =0 and another answer.
You get t = 0 because it starts off on the ground - solving for "s = 0" solves for all times "t" when the rocket is on the ground.

You're also dealing with a second-order equation, or a quadratic equation. This means that it will have two "real" answers. For third order and fourth order, you'll have three and four real solutions. You don't need to know this for this problem, but it's worth noting for the future. ;)