Advanced MathEasy–MediumWhen a projectile returns to the ground
Advanced Math practice question
The height, in feet, of a model rocket t seconds after it is fired from the ground is modelled by h(t) = −16t² + 64t. How many seconds after firing does the rocket return to the ground?
Answer: 4
On the ground, h(t) = 0: −16t² + 64t = 0, so −16t(t − 4) = 0. Either t = 0 (the launch) or t = 4. The rocket lands 4 seconds after firing.
Common wrong answers
- If you answered 0
- t = 0 is the moment of firing — the rocket is on the ground then too, but the question asks when it RETURNS.
- If you answered 2
- 2 is when the rocket reaches its HIGHEST point (halfway through the flight), not when it lands.
- If you answered 64
- 64 is the height, in feet, at the peak (h(2) = 64), not a time.
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