2. The distance traveled by a falling object is given by the formula d = 0.5gt2 where d = distance, g = the force of gravity, and t = time. Solve this equation for g, and use your formula to determine the force of gravity if a baseball takes 10 seconds to hit the ground after being dropped from a height of 490 feet. Show all steps in your work.

Question

2.	The distance traveled by a falling object is given by the formula d = 0.5gt2 where d = distance, g = the force of gravity, and t = time. Solve this equation for g, and use your formula to determine the force of gravity if a baseball takes 10 seconds to hit the ground after being dropped from a height of 490 feet. Show all steps in your work.

anonymous · Answer

I know this is an algebra question, but it's bugging me: $g$ doesn't represent *force* of gravity, but the *acceleration* due to it.

Anyway, the equation given is
$$d=\frac{1}{2}gt^2$$
We want to solve for $g$:
$$\begin{align*}d&=\frac{1}{2}gt^2\
2d&=gt^2&\text{multiply both sides by 2}\
\frac{2d}{t^2}&=g&\text{divide both sides by }t^2
\end{align*}$$
and that's all there is to that.

anonymous · Answer

Now, you want to determine the value of $g$ given the info about the baseball. It takes 10 seconds for it to hit the ground, so $t=10$. It's dropped from a height of 490 feet, so $d=490$.

Plug in the numbers and compute:
$$g=\frac{2(490)}{10^2}=\cdots$$