Question

Given a baseball is hit from the ground with an initial velocity of 48 ft/s.

Create a function that can be solved, where h is the height of the ball at time t in seconds.

Answer 1

The function that describes the height h of a baseball at time t after being hit from the ground with an initial velocity of 48 ft/s is h(t) = -16 * t^2 + 48 * t. This formula takes into account the acceleration due to gravity which is 32 ft/s^2.

Step-by-step explanation:

To create a function that describes the height h of a baseball at time t in seconds after being hit from the ground with an initial velocity of 48 ft/s, we use the physics formula for the vertical motion of projectiles under gravity. The general formula for height as a function of time is given by:

h(t) = -1/2 * g * t2 + V0 * t + h0

Where:

g is the acceleration due to gravity (32 ft/s2 for gravity in feet per second squared)

V0 is the initial velocity (48 ft/s in this case)

h0 is the initial height (0 ft since it is hit from the ground)

Therefore, the function for the height h of the baseball at time t is:

h(t) = -16 * t2 + 48 * t

This quadratic equation can be solved for different values of t to find the height of the baseball at any given time.