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When chasing a hare along a flat stretch of ground, a greyhound leaps into the air at a speed of 10.0 m/s, at an angle of 31.0 above the horizontal. (a) What is the range of his leap and (b) for how much timeis he in the air?

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Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

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.

03:10

When chasing a hare along …

01:34

01:44

01:28

02:44

70. When chasing a hare al…

02:36

when chasing a hare along …

06:07

A gray kangaroo can bound …

05:54

A running mountain lion ca…

04:29

A squirrel completing a sh…

04:38

03:21

A stuntman sitting on a tr…

02:14

\cdots An airplane is flyi…

01:19

A skydiver deploys his par…

02:01

A kangaroo can jump over a…

So the question states that a dog jumps in the air a speed of 10 meters per second, an angle of 31 degrees. And we're trying to find how long the dog is in the air for as well as how far he Jones. So to figure out how far he jumps, we first need to figure out how long he's in the air. Four. Um, And to do this, we can first separate this velocity vector into two components of Visa, vex and visa. Why? And to figure out what these are, um, we could use just use trigonometry. So the sign of 31 degrees is equal to opposite over high pot news. So visa, Why over 10. So that means fee supply is equal to 10 times sign of 31 degrees, and same thing goes for co sign of 31 degrees. It's adjacent over iPod news v sub X, over 10. So that would give us Visa of X is equal to um 10 co sign of 31 degrees. So now that we have this, we can use our kin Matics equations to so for the time. So the one that we should use. Ah is the one that states that the change in displacement is equal to the initial velocity turns time plus one have times the acceleration time to the Times Square. Um, and for this case, we really just need a folks on the vertical component of the velocity to give us the time. So the displacement in the vertical vertical direction is just gonna be zero because dog's gonna jump from the ground and land on the ground. The initial velocity in the vertical direction is 10 sign 31 degrees. This multiplied by t plus 1/2 times the acceleration, which is negative 9.8 due to gravity times the Times Square. So we can factor out a t here and we'll get 10 sign 31 degrees close 1/2 times negative, 9.8 t times t. And when we saw for tea, we can see that T is either equal to zero or tea will be equal to 1.0 51 seconds. So this T equals zero. Doesn't it? Doesn't make any sense. So we can give her to this. And the correct route is this one. So now that we have the time we can figure out the range that Thea dog jumps in the Air Force. So how far he travels? Um, and we can just use the formula, which states that the velocity times the time is equal to the Ranger, the displacement in the X direction. So the horizontal velocity we calculated here. So we complied this in, and we also know the time we complete this in as well. And once again, this is the correct formula to use because there's no acceleration in the X direction. Um and so when we plugged this in, we figure out that the range is equal to 9.1 years, and that's the

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