Functions and Relations Question
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Grade 10 Functions and Relations CCSS: HSF-IF.C.9
Shawn's class has been learning about rockets and is planning to launch a small model rocket of their own. The rocket will be launched from ground level, straight up into the air. The rocket does not have a parachute. The class has determined the theoretical height and time of the rocket's flight, as modeled by the following function.
f(t)=-5t2+100t
For this function, f(t) is the height of the rocket in meters, and t is the duration of the flight in seconds. When they actually fire the rocket, it lands 18 seconds after it was fired. Shawn was on top of a nearby structure that is 35 meters high. He measured that the rocket, as it ascended, passed him 0.5 seconds after it launched.
Was the theoretical calculation correct, in terms of the maximum height of the rocket? If not, by how much did it over- or underestimate the rocket's maximum height?
f(t)=-5t2+100t
For this function, f(t) is the height of the rocket in meters, and t is the duration of the flight in seconds. When they actually fire the rocket, it lands 18 seconds after it was fired. Shawn was on top of a nearby structure that is 35 meters high. He measured that the rocket, as it ascended, passed him 0.5 seconds after it launched.
Was the theoretical calculation correct, in terms of the maximum height of the rocket? If not, by how much did it over- or underestimate the rocket's maximum height?
- The theoretical calculation was correct, the rocket reached a maximum height of 500 m.
- The theoretical calculation underestimated the height by 140 m.
- The theoretical calculation overestimated the height by 419 m.
- The theoretical calculation overestimated the height by 176 m.