2) (10 points) If the vertical velocity of a jumping jackal...

2) (10 points) If the vertical velocity of a jumping jackal is given by h(t) = 15t - 4.9t$^2$ meters per second, compute the average velocity of the jackal over the time interval [1, 1.05] (in seconds), use units in your answers.

Transcript

0:00 There.

00:01 So for this problem, the function that we are given is for the height.

00:08 Now the height in terms of the time is 51 times the time this minus 0 .83 times the time square.

00:31 So we need to find the average velocity over the given time in intervals.

00:37 So we are given a time interval from 2 to 3, 2 to 2 .5, and some other values.

00:48 So i'm going to calculate some of them, and you will just do the same for the other values.

00:55 So let's start with the interval 2 to 3.

01:01 Now, for this we can identify that the initial time is equal to 2, and the final time is 3.

01:07 So the average velocity or average speed is equal to the function that we are given evaluated at the final time minus the function that we are given, which is the function of position, evaluated at the initial time.

01:30 This divided by the difference between this time, so that will be the final time minus the initial time.

01:37 Now we evaluate the function that we are given at this time, so that will be 51 times 3, this minus 0 .83 times 3 to the square.

01:53 And this minus, this function evaluated at the initial time, so that will be 51 times 2, this minus 0 .83.

02:09 Well, it should be plus in here times 2 to the square.

02:15 And then we divide this by the difference between these two values.

02:19 So that will be 3 minus 2.

02:24 So using our calculator, we obtain a value of.

02:32 So the value that we obtained from this is 46 .85.

02:40 This should be in units of meters per second.

02:49 So once we know that, that will be our average speed or velocity in this interval of time.

03:01 Now we can pass to the other interval of time...

Question

2) (10 points) If the vertical velocity of a jumping jackal is given by h(t) = 15t - 4.9t$^2$ meters per second, compute the average velocity of the jackal over the time interval [1, 1.05] (in seconds), use units in your answers.

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