Question

A man throws a ball off the top of a building. The table shows the height of the ball at different times.
Time: 0 s at 46 feet
1 s at 63ft
2 s at 48 ft
3 s at 1 ft
A. Find a quadratic model for the data
B. use the model to estimate the height of the ball at 2.5 seconds

Answer 1

Here on Earth, the value of the acceleration of gravity is pretty well known and more or less constant. That means a projectile in free flight with aerodynamic effects ignored moves by the function\[s(t)=-16t^2+v_0t+s_0\]with vsub0=initial velocity and s sub0 =initial height. Since we are given s sub0 and s(1), we can solve easily for vsub0. After that, solving the problem is a matter of substitution.