A ball with mass 0.3 kg is thrown upward with initial...

A ball with mass 0.3 kg is thrown upward with initial velocity 20 m/s from the roof of a building 100 m high. Assume there is a force due to air resistance of magnitude $\frac{|v|}{30}$ directed opposite to the velocity, where the velocity $v$ is measured in m/s. NOTE: Use $g=9.8 \text{ m/s}^2$ as the acceleration due to gravity.

Transcript

00:01 Okay, we have a ball being thrown off the building, 30 meters tall, and it's going to have an upward velocity of 20 meters per second.

00:07 You know that it's going to kind of follow that path all the way down, so it's going to go up and then back down.

00:12 So we have to find a few things first.

00:15 We want to try to find the maximum height.

00:19 So, again, a few things i do know.

00:21 I do know that the initial velocity is 20 meters per second.

00:24 It's positive because it's going straight up.

00:26 I know that at a maximum height velocity must be zero because whenever i reach a maximum value, i stop before i start coming back down.

00:34 So maximum height, always a velocity of zero.

00:37 And since this is in free fall, there's no other force outside of gravity acting on it.

00:41 It's going to be negative 10 meters per second square.

00:44 Your teacher might also tell you negative 9 .8, but i'm judging by the nice round numbers here, i'm thinking negative 10 would be fine just as well.

00:52 So i'm looking for the max height, so my change in my y position, and i'm looking for an equation that does not include time.

01:02 So that equation looks like so.

01:06 And these are your kinematic equations that you would have.

01:10 So now let's plug in our values.

01:12 The velocity is zero.

01:14 Initial velocity was 20.

01:16 My acceleration is negative 10, and i'm looking for delta y.

01:22 I finish up my algebra and i get an answer.

01:27 Now remember the building was also 30 meters tall.

01:34 So after i solve for this delta y, i need to include the height of that building.

01:43 So when i do my algebra, i got a displacement of 20 meters.

01:47 But again, the building is also 30 meters tall.

01:50 So my height from the top of the ground would be 50 meters, 30 meters plus the 20 meters i went up.

01:58 For part b, we're trying to find the total time that it's moving.

02:01 Now, my displacement is going to be negative 30 because, again, it's going to start here.

02:05 That's my initial position.

02:07 It's going to end here.

02:07 That's my final position.

02:09 So remember that the path it takes does not matter when we talk about displacement.

02:13 So it's going to go down 30 meters...

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