The height above the ground of a stone thrown upwards is given...

Question

The height above the ground of a stone thrown upwards is given by s(t), where t is measured in seconds. After 1 second, the height of the stone is 48 feet above the ground, and after 1.5 seconds, the height of the stone is 60 feet above the ground. Evaluate s(1) and s(1.5), and then find the average velocity of the stone over the time interval [1, 1.5].

Accepted Answer

Welcome back, everyone. A ball is thrown vertically upwards and its height above the ground is given by the function H of T, where T represents time in seconds. At T equals 2 seconds, the ball's height is 80 ft. And at T equals 3 seconds, its height is 100 ft. Determine the values of each of 2 and H of 3, and calculate the average velocity of the ball over the time interval from 2 to 3 seconds. So first of all, let's understand that it says a T equals 2 seconds. The ball's height is 80 ft. So this is defined by the function H of 2. Height at 2 seconds is 80 ft. So H of 2 equals 80 ft, and we have the first answer. Now we want to identify H of 3. So this is height at time of 3 seconds, and according to the context of the problem at T equals 3 seconds, its height is 100 ft, and we have the second answer to this problem. Now let's calculate the average velocity of the ball, and let's recall that the average velocity is the change in height divided by the change in time. In this case, we take the final height H2. And in this case, our final height is age of 3. We subtract the initial height at age of 2, and we divide by the change in time. So time. Or basically the final time value, which is T2, that's 3 seconds. Minus 2 seconds, right, because the initial time of interest is 2 seconds. So essentially the average velocity can be calculated as each of 3, which is 100 ft. Minus 8 of 2, which is 80 ft. And we are subtracting that by the difference between 3 seconds and 2 seconds. So we get 20 divided by 1, which is 20. Feet per second, so the average velocity. Would be equal to 20 ft per second. And those be our final answers. Thank you for watching.

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