Question

If a ball is thrown straight up into the air with an initial velocity of 60 ft/s, its height in feet after t seconds is given by y=60t−16t^2. Find the average velocity for the time period beginning when t=1 and lasting: (i) 0.5 seconds:

(ii) 0.1 seconds:
(iii) 0.01 seconds: (iv) 0.0001 seconds:

Answer 1

To find the average velocity for a given time period, we need to calculate the displacement and divide it by the time interval. In this case, the height function is y = 60t - 16t^2.

Step-by-step explanation:

To find the average velocity for a given time period, we need to calculate the displacement and divide it by the time interval. In this case, the height function is y = 60t - 16t^2. We can find the average velocity by determining the change in height (displacement) during the time interval and dividing it by the duration of the interval.

(i) For a time period of 0.5 seconds:

Initial height, y1 = 60(1) - 16(1^2) = 44 ft

Final height, y2 = 60(1.5) - 16(1.5^2) = 30 ft

Displacement = y2 - y1 = 30 - 44 = -14 ft

Average velocity = Displacement / Time = -14 ft / 0.5 s = -28 ft/s

(ii) For a time period of 0.1 seconds:

Follow the same steps as above to find the displacement and calculate the average velocity.