Two balls are rolled off a tabletop that is 0.8 m above the...

Two balls are rolled off a tabletop that is 0.8 m above the floor. Ball A has a horizontal velocity of 3 m/s and that of ball B is 5 m/s. a. Assuming g = 10 m/s^2, how long does it take each ball to reach the floor after it rolls off the edge? b. How far does each ball travel horizontally before hitting the floor? c. If the two balls started rolling at the same time at a point 1.2 m behind the edge of the table, will they reach the floor at the same time? Explain.

Transcript

00:01 Are being launched from a table.

00:02 The table has a height of 0 .8 meters, and the balls have two different speeds.

00:08 And so this is going to be a projectile motion problem.

00:10 So i'm going to separate by givens in the horizontal and vertical.

00:14 So we know for the vertical, the initial velocity for a horizontal projectile is zero, because it's just moving horizontally.

00:19 The acceleration is going to be negative 9 .8 meters per second squared, and that's because of gravity.

00:26 That's the only acceleration in the vertical.

00:28 And it's displacement.

00:30 Is going to be that 0 .8 meters, but it's moving downward, so that is negative.

00:35 Now we have velocity of ball a and ball b.

00:39 And so i'm going to go ahead and put them in the same spot, but just know you're treating them like two different things.

00:44 So ball a has three meters per second horizontal velocity, and ball b has five meters per second.

00:51 And so the first thing we want to know is, assuming gravity is 10, actually.

00:56 So let's go ahead and make this negative 10, which makes our number so much more beautiful.

01:01 We want to know how long does it take for each ball to fall? well, the time of fall is not determined by the horizontal velocity.

01:09 It's determined by the height.

01:11 And that's because there's gravity in the horizontal.

01:15 And so the equation we're going to use for this is displacement.

01:18 It's equal to initial velocity times time plus one -half acceleration time squared.

01:24 And so none of this is from the horizontal.

01:26 And so actually they're going to land at the exact same time because they're being released from the same height.

01:31 This initial velocity is simply zero.

01:33 So we have negative 0 .8 is equal to 1 1�t times negative 10, t squared.

01:40 So we have 0 .8 is equal to negative 5, t squared...

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