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SSM An airplane is flying with a velocity of 240 …

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Problem 42 Hard Difficulty

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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Video Transcript

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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Problem

SSM An airplane is flying with a velocity of 240 …

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Watch More Solved Questions in Chapter 3

Video Transcript

John D. Cutnell, Kenneth W. Johnson

Physics

Elyse Gonzalez

Andy Chen

Aspen Fenzl

Jared Enns

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics

Elyse Gonzalez

Andy Chen

Aspen Fenzl

Jared Enns

John D. Cutnell, Kenneth W. JohnsonPhysics

Elyse Gonzalez

Andy Chen

Aspen Fenzl

Jared Enns

John D. Cutnell, Kenneth W. Johnson

Physics