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In the javelin throw at a track-and-field event, the javelin is launched at a speed of $29 \mathrm{~m} / \mathrm{s}$ at an angle of $36^{\circ}$ above the horizontal. As the javelin travels upward, its velocity points above the horizontal at an angle that decreases as time passes. How much time is required for the angle to be reduced from $36^{\circ}$ at launch to $18^{\circ} ?$

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Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Cornell University

University of Michigan - Ann Arbor

University of Sheffield

University of Winnipeg

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.

02:13

The range of a projectile …

02:34

Projectile Motion The rang…

02:35

03:23

Solve each problem.Thr…

02:54

$$\text { The range of a p…

01:50

A projectile launched from…

02:51

A second baseman tosses th…

04:25

An Olympic long jumper lea…

00:49

A quarterback throws a foo…

03:35

In a friendly game of hand…

So the question states that a javelin is thrown at a 36 degree angle with a speed of 29 meters per second, and we're trying to find at what time, after the gentle in his throne, the angle of the velocity vector is equal to 18 degrees. So the first thing we should really do is separate our velocity into a visa, Becks and a visa Y, um and we know that we can do this because co sign of 36 degrees is equal to adjacent over high pot news. And the adjacent in this case is Visa Vex. So the subjects over 29 which means Visa Becks, is equal to 29 times co sign of 36 degrees, and the same thing goes for Visa y. But instead of co sign, it will be signed. So now that we know what Visa Becks is and Visa, why is we can, um, go on with the problem? So we know at a time t The horizontal velocity of the projectile isn't going to change because there's no acceleration in the X direction. So once the angle of velocity vectors 18 degrees visa, Becks will still be 29 times co sign 36 degrees. So now that we know that we can figure out what our visa why is And once we figure out what V supply is when the angles 18 degrees, we can figure out the time, um, at which this happens. So to figure out what the supply is, we can use the following relationship that the tangent of 18 degrees is equal to opposite over adjacent. So the opposite in this case is visa. Why? And the adjacent in this case is 29 times co sign of 36 degrees. And when we plug everything in and solve, we find that visa by is equal to seven point 6 to 31 meters per second. So now that we have Visa Y, you can use our kingdom attic equation, which states that the final velocity let's say in the Y direction for this case is equal to the initial velocity in the Y direction, plus the acceleration times the time. So we know the final velocity when the angle of the magnitude of the velocity is 18 degrees is 7.6231 meters per second. We know the initial vertical velocity is 29 times sign of 36 degrees. We know that the acceleration is negative, 9.8 meters per second squared due to gravity. And we're trying to sell for tea. So when we subtract 29 times, sign 36 on both sides and then divide by negative 9.8 on both sides we find that T is equal 2.96 seconds.

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