Question

A baseball player hits a home run. Which type of function would best represent the height of the ball over time?

a. linear function
b. quadratic function
c. exponential function
d. both a. and b.

Answer 1

b. quadratic function

Explanation:

If a baseball player hits a home run, the function that best represent the height of the ball over time because this is a problem of projectile motion, a type of motion we get when an object is thrown near the Earth's surface, so it moves along a curved trajectory affected just by the action of gravity, if we ignore the air resistance. So that function follows the form:

`h(t)=-(1)/(2)gt^2+v_(0)t+h_(0)`

Where:

`h(t) \ is \ the \ height \ of \ the \ ball \ at \ any \ time \\ \\ g \ is \ the \ gravitational \ acceleration \\ \\ v_(0) \ is \ the \ initial \ velocity \ of \ the \ ball \\ \\ h_(0) \ is \ the \ initial \ height \ of \ the \ ball`

As you can see, this function is a parabola that opens downward.