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A golf ball rolls off a horizontal cliff with an initial speed of 11.4 m/s. The ball falls a vertical distance of 15.5 m into a lake below. (a) How much time does the ball spend in the air? (b) What is the speed v of theball just before it strikes the water?

(a) $t=1.78 \mathrm{s}$(b) $v=2084 \mathrm{m} \cdot \mathrm{s}^{-1}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

Hope College

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

03:43

A golf ball rolls off a ho…

02:26

01:55

(a) How long does it take …

04:05

A golfer tees off from the…

06:59

A ball is thrown horizonta…

08:03

A golf ball is dropped fro…

04:11

A golf ball is hit on leve…

08:26

10:15

A golf ball with an initia…

05:08

02:44

A Small Ball A small ball…

03:00

A small ball rolls horizon…

So the question states that a ball is rolling off the edge of a cliff horizontally at 11.4 meters per second and the cliff is 15.5 meters tall. And we're trying to find how long the ball will stay in the air four as well as what the final velocity is of the ball. So to do this, we can just use our kingdom attics formulas. So the 1st 1 we should look at is the one that states that the change in displacement is equal to the initial blast. He turned to time plus 1/2 times the acceleration times the time squared. And so we know that the, uh, change in displacement in the vertical direction. So this using this equation in the vertical direction that changing this placement in the vertical direction is going to be negative 15.5 meters. We know that the initial loss in the vertical vertical direction is zero. So this term is going to cancel out. We also know that the acceleration in the vertical direction is negative 9.8 due to gravity. And we have t square attack there on the end so we can solve for T and will find that he is equal to 1.7 a seconds. Just this is our time t the time that the ball is in the Air Force and we just did this by dividing by 1/2 times negative 9.8 almost side and then taking this courtroom. So now that we have the time, let's look at right before the ball hits the water. So the velocity vector is going to look something like this. It's gonna be at some sort of angle from the horizontal, and we know for a fact that are horizontal velocity vector is going to be 11.4 meters per second and this is due to the fact that the ball is undergoing projects out motion. So there's no acceleration in the X direction and so the velocity is constant. And if we want to find this vector the year, we either need to find what this angle here that we're calling data is, or the vertical component of the velocity right before it hits the water. And the easiest thing to do is probably find this component here. So to do this, we can just use our, um equation, which states that the philosophy, the final velocity is equal to the initial velocity, plus the acceleration times the time. So we know the initial vertical velocity is zero. So this term canceled and we know the time and the acceleration. So we're gonna say V is equal to negative 9.8 times the time 0.78 seconds and we get this vserv y is equal to 17 negative 17 point for two meters per second. And so now that we know what our our visa vexes and our visa, why is we can find the magnitude of this capital vector B. So the magnitude of vector V is defined as the square root of bees of X squared, plus visa y squared. And when we plug in Visa, Becks and Visa buy into this equation, we that we get that Capital V is equal to 20 0.83 meters per second, and that's the final answer

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