A moderate wind accelerates a pebble over a horizontal xy...

A moderate wind accelerates a pebble over a horizontal xy plane with a constant acceleration $\vec{a} = (5.12\hat{i} + 7.86\hat{j})$ m/s². At time t = 0, the velocity is $(3.07\hat{i})$ m/s. What are the (a) magnitude and (b) angle of its velocity when it has been displaced by 12.7 m parallel to the x axis? (a) Number Units m/s (b) Number Units ° (degrees)

Transcript

00:01 In this problem, we want to find the direction and the magnitude of the velocity after some object has moved 12 meters in the x -axis with this initial velocity and this acceleration.

00:15 So let's begin by finding the x and y components of velocity.

00:20 We know that velocity squared is equal to initial velocity plus two times the acceleration times the displacement.

00:32 And we know the displacement in the x -axis.

00:35 So let's use this equation to find, or oops, this should be square.

00:40 Yeah.

00:41 Let's use this equation to find our x quantities.

00:46 So the velocity in the x -axis is going to be equal to the square root of the initial velocity in the x -axis plus two times the acceleration times the displacement.

01:00 And we have all this information.

01:02 We have the initial velocity over here.

01:05 That's four squared plus two times the acceleration in the x -axis which is five and then we are told that the displacement is 12 meters along the x -axis so this velocity is going to give us roughly 11 .7 meters per second now we cannot use the same equation to find the y component because we don't know the displacement in the y -axis and it would probably take a while to solve for the displacement so it's easier to find the time it took to an object to move to this speed in that displacement.

01:49 So let's use this equation to find that time instead.

01:56 Let's use some blue.

01:58 We can say that the displacement in the x -axis is equal to one -half times the velocity in the x -axis plus the velocity, the final velocity in the x -axis times the time.

02:14 So here we have our time...

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