Thread: Quadratic Function that Models Height

A rocket is launched in the air from the ground and is 100 ft high after 1 second. After 2 seconds it is 280 ft high. Which of the following is the quadratic function that models its height h(t) after t seconds?

a...h(t)= 60t^2+40t
b.. h(t)=40t^2 + 60t
c...h(t)= 60t^2-40t
d...h(t)= 40t^2-60t

I am not looking for simply the answer. I want to you how to find it from the list provided.

Hello, nycmath!

A rocket is launched in the air from the ground and is 100 ft high after 1 second.
After 2 seconds, it is 280 ft high.
Which of the following is the quadratic function that models its height h(t) after t seconds?

. . $\displaystyle \begin{array}{c}(a)\;h(t)\:=\:60t^2+40t \\ \\[-4mm] (b)\;h(t)\:=\:40t^2 + 60t \\ \\[-4mm] (c)\;h(t)\:=\: 60t^2-40t \\ \\[-4mm] (d)\; h(t)\:=\: 40t^2-60t \end{array}$

We are told that: .$\displaystyle h(1) = 100,\;h(2) = 280$

Determine which of the functions produces those values.

This is an arithmetic problem! Set t= 1 and t= 2 and calculate the values.

Originally Posted by nycmath

A rocket is launched in the air from the ground and is 100 ft high after 1 second. After 2 seconds it is 280 ft high. Which of the following is the quadratic function that models its height h(t) after t seconds?

a...h(t)= 60t^2+40t
b.. h(t)=40t^2 + 60t
c...h(t)= 60t^2-40t
d...h(t)= 40t^2-60t

I am not looking for simply the answer. I want to you how to find it from the list provided.

If you are thinking there may be a more physical way to solve this (hey, it's a height vs. time problem after all) there isn't one. The accelerations aren't physical, at least near the Earth anyway.

-Dan

I can take it from here. Thanks.