# A batter hits a fly ball. A scout in the stands makes the following observations. time     | .75  | 1.5  |   2  | 2.75 | 3.25 | 4.75 | height    |  77  | 133 | 160 | 187 |  194  | 169...

A batter hits a fly ball. A scout in the stands makes the following observations.

time     | .75  | 1.5  |   2  | 2.75 | 3.25 | 4.75 |

height    |  77  | 133 | 160 | 187 |  194  | 169 |

I think the best-fit equation is -15.9x^2 + 110.48x + 3.02

Determine the initial velocity of the baceball and the height of the ball when hit. Round to the nearest hundredth.

Asked on by loishy

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Your equation is the best-fit quadratic. So we have `y=-15.9t^2+110.5t+3.02`

Assuming that the measurements were in feet, the height of the ball when hit is approximately 3.02 ft. (The ball is hit at time t=0.)

The velocity is the rate of change of height per unit of time. This is found using the first derivative:

`y'=-31.8t+110.5` . At time t=0 the velocity is 110.5 ft/sec.

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Another way of seeing this is the model `y=-1/2 g t^2+vt+y_0` where g is the gravitational constant ( 32 feet per second squared when using standard units instead of metric units), v is the initial velocity and `y_0` is the initial height.

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