Determine the initial velocity and height of the ball when hit. Round to the nearest hundredth.
Using this linear regression
y=-15.9t^2 + 110.48t + 3.02
And this vertical motion model
h= -16t^2 + vt + s
where t is time (in seconds) the object has been in the air, v is the initial vertical velocity (in feet per second), and s is the initial height (in feet).
I figured out the height was 3.02, but I can't figure out the initial velocity.
Assuming that you have some data (provided in a table or obtained using a CBL or equivalent equipment) on the position of the ball at various times t, it seems that a quadratic regression has yielded `y=-15.9t^2+110.48t+3.02 ` where y is the height of the ball and t is time in seconds.
Comparing to the vertical motion model `y=-16t^2+v_0t+y_0 ` where `v_0 ` is the initial velocity and `y_0 ` is the initial height we get:
initial height 3.02 feet
initial velocity 110.48 feet per second.
The difference in the leading coefficient is probably due to measurement error, including the fact that the force of gravity is not constant on the surface of the earth. The initial velocity is positive, indicating the ball initially went away from the ground, reached some maximum height, and then returned to the ground.