
Math in the real world
We throw a rock into the air with initial velocity of 96 ft/sec, and initial position of 5 ft. Find how high the rock goes before coming back down. To answer this question, fill in the blanks in the following sentence, where the first blank gives this height, and the second blank gives how many seconds into the flight of the rock it reaches this maximum height.
The rock reaches its highest position of _______ feet above the ground after _______ seconds of flight
How can solve this problem?

You can use the formula $\displaystyle v_f^2=v_i^2 + 2 a \Delta s $
You know what you final velocity is (at the top), the initial velocity as well and a is the gravitational acceleration. Solve for $\displaystyle \Delta s $to find the displacement and don't forget to add the initial height.
Then you can use $\displaystyle \Delta s = v_i \Delta t+ \frac{a \Delta t^2}{2} $ and solve for t to find how long it took.

i would also draw your self a diagram so that you can see yourself what is really happening. the maths in questions like this is usally easy but the prob is to find out what way to do it. after that you just fill into you formula.