Q2 (a) (1 point) The height (in meters) of a golf ball 't'...

Q2 (a) (1 point) The height (in meters) of a golf ball 't' seconds after it has been hit into the air, is given by H(t) = 20t - 5t^2. Determine the following: (a) The average vertical velocity of the ball during the first two seconds. Q2 (b) (3 points) b) The vertical velocity of the ball at an arbitrary time t. Q 2(c) (2 points) c) Find the vertical velocity with which the ball hits the ground.

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00:01 Here we're given the equation h of t, which describes the height of a golf ball, and that's going to be 20t minus 5t squared.

00:11 So first off, we want to find the average vertical velocity of the ball during the first two seconds.

00:17 So what we have to do then is find the height at two seconds minus the height at zero seconds, and divide that by two minus zero.

00:28 So here, the height at two seconds means just plug in two here and i'm going to get 20.

00:36 So two seconds later, it's going to be at a height of 20.

00:41 Minus now at zero, well, it didn't go anywhere to start with, so it's zero.

00:46 So the average is 20 over 2, which is 10.

00:50 That is the average velocity over the first two seconds.

00:54 Now for part b, we need to find the vertical velocity of the ball at any arbitrary time.

00:59 That's just going to be the derivative v of t, which is 20 minus 10t, because i took the power rule.

01:12 So now for part c, we need to find the vertical velocity for which the ball hits the ground.

01:17 Well, this is a two -part question.

01:19 We really need to know when does it hit the ground and what's its velocity there? so i'm going to take this 20t minus 5t squared and set it equal to zero.

01:28 To do that, i'm going to pull out a 5 and a t.

01:33 So i'm left with a 4 t minus 5...

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