Question

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 48ft/s. Its height in feet after t seconds is given by y=48t−11t^2. Find the average velocity for the time period

Answer 1

To find the average velocity for a ball thrown into the air on an alien planet, use the height equation y=48t−11t^2 and apply it at two different times to determine displacement. The average velocity is then the change in displacement divided by the change in time.

Step-by-step explanation:

The question involves calculating the average velocity for a ball thrown into the air with a given initial velocity and a described height-time relationship. The formula for the ball's height is provided as y=48t−11t2. To find the average velocity for a given time period, we need to consider the change in displacement over the change in time.

To calculate the average velocity for a time period t1 to t2, we would use the height function y(t) to determine the positions at those times and then compute the average velocity using average velocity = (y(t2) - y(t1))/(t2 - t1).

For example, if a student needs to find the average velocity between t=1s and t=3s, they would need to plug these values into the height equation to get y(t=1) and y(t=3), and then compute the average velocity using the formula above.