Question

A baseball is hit, and it flies through the air, and is a foul ball. It is caught in the seats near first base at a height of 18 feet. The equation relating the height over time is y= -16x^2+160x+4. In feet per second, what was the starting vertical speed when the baseball was hit?

Answer 1

The starting vertical speed of the baseball was 160 feet per second, which is derived from the coefficient of the x term in the quadratic equation representing the height of the baseball over time.

Step-by-step explanation:

The equation given for the height of a baseball over time is y = -16x^2 + 160x + 4, which is a quadratic equation.

To find the starting vertical speed when the baseball was hit, we need to determine the coefficient of the x term in the equation.

This coefficient represents the initial velocity in the vertical direction because the general form of the equation for such motion is y = -16t^2 + v0t + y0, where v0 is the initial velocity, and y0 is the initial height.

In the provided equation, the initial velocity v0 is represented by the coefficient 160. Therefore, the initial vertical speed of the baseball was 160 feet per second.