Final answer:
To find the average velocity of an object thrown straight up, you need to calculate the change in height and the time it takes to reach that height. Then, you can divide the change in height by the time to find the average velocity.
Step-by-step explanation:
The height of an object thrown straight up from a height 5 feet above the ground is given by the equation h(t)=-16²+42t+5, where t is the time in seconds after the object is thrown. To find the average velocity of the object, we need to calculate the change in height and the time it takes for the object to reach that height. In this case, we want to find the average velocity over a specific time interval. Here are the steps:
- Calculate the initial height of the object: h(0) = -16(0)² + 42(0) + 5 = 5 feet
- Calculate the final height of the object after a certain time interval: h(t) = -16t² + 42t + 5
- Subtract the initial height from the final height to find the change in height: Δh = h(t) - h(0)
- Find the time it takes for the object to reach the final height: Solve the equation h(t) = final height for t
- Calculate the average velocity using the formula: average velocity = Δh / t
Remember to use the positive root of the quadratic equation as the time value, as the negative root represents a time before the object was thrown.