If a ball is thrown vertically upward from the ground with a...

If a ball is thrown vertically upward from the ground with a velocity of 144 ft/s, then its height after t seconds is s = 144t - 16t^2. What is the maximum height reached by the ball? ft What is the velocity of the ball when it is 320 ft above the ground on its way up? (Consider up to be the positive direction.) ft/s What is the velocity of the ball when it is 320 ft above the ground on its way down? ft/s When will the ball hit the ground? t = s With what velocity does the ball hit the ground? ft/s The position function of a particle is given below. s(t) = t^3 + 3t^2 - 21t, t ? 0 When does the particle reach a velocity of 3 m/s? t = s

Transcript

00:03 Now in this question, we have ball, which is throwing vertically upward from the ground with the velocity of this much, and the height, it's height up to 2 seconds, given by this, right? and you're asking what is the maximum height to reach by the ball? well, the maximum height is reached when the ball has velocity been zero, right? so the velocity is given by s prime, right? the derivative, which is given by 1 ,44, minus 32t, right? now you said this to be zero, and you'll find t equals what? and that's 1 -444, divided by 32, right, which gives you actually 4 .5 seconds, right? 4 .5.

00:39 Now you're plugging 4 .5 into this separation, then you get the height, right? that's, of course, given by 1 -44 times 4 .5 minus 16 times 4 .5 squared, which gives you 300, 324 feet, right? what is velocity ballwind is this much above the ground on its way up, right? so weight s is this much, right? and actually you can see that, you ask you ask for the velocity, right? and you ask you the velocity, philosophy, as we say, it's given by this, right? and now you look at weighing basically the fate, the height is 320, right? so that is s equals 320.

01:23 What we need to do, of course, is just to find the solution, right? so suppose s equals 32, that means 140 t.

01:30 Minus 16 squared equals 320, right? and then from this, we can find, of course, the time t, right? so basically we found the time t equals, we can find the time t, right? the time t, you will find this two solutions.

01:50 You will find this actually be given by, you know, we can rewrite this a little bit like 16t squared, right, minus 1 -44t, right? and then plus 320, right? the super zero, right? and then we see that t is actually given by, t is actually given by, you know, two times 16, right, using the formula, right? and one, 14 plus minus the two possible values, one corresponding upward motion, that gives you a downward motion, right? and b squared 1 ,44 squared, minus four times 16 and times 220, right? now if you do the calculation, you'll find, this to be actually given by.

02:32 So it's given by 1 -44 -4.

02:34 Let's look at the plus -line first, and the squared load of 1 -44 -square minus 4 times 16 times 320, right? and then you divide this, of course, by 32, and actually gives you 5.

02:49 The first is 5, but another one is you take the minus sign.

02:53 You'll find this to be actually given by 4, right? 4.

02:58 So i'll get upward corresponding to t -5...

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