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. Show that a projectile achieves its maximum range when it is fired at $45^{\circ}$ above the horizontal if $y=y_{6}$

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Physics 101 Mechanics

Chapter 3

Motion in a Plane

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rutgers, The State University of New Jersey

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Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

02:22

Show that for a projectile…

05:25

Show that, for a given ini…

06:15

Show that a projectile rea…

06:29

A projectile launched at a…

03:29

A Projectile A projectile…

10:25

A projectile is launched w…

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A projectile is shot in th…

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Find the range $R$ and max…

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Find the launch angle for …

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A projectile is launched a…

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Path of a Projectile When …

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A projectile thrown from a…

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A projectile has horizonta…

01:57

16:06

For the general projectile…

02:23

The range of a projectile …

02:10

06:04

Height versus time Show th…

03:25

A projectile is fired with…

07:14

A projectile is launched f…

so the rain. If given that delta y equals zero meters per second, which angle gives the highest range, So the ranges equaling the initial squared sine of tooth ada divided by G now are Max occurs when sign of two theta equals one, and this is because I sign any sign function, fluctuates between negative won and won. So, in order, get the maximum value of the range. Essentially, you want the maximum value of the sine function and, in every case, the maximum value of a trick in the mix of a trigger and a metric function. Ah, rather of a sine function or co sign function is going to be one. So our max occurs when sign of two theta equals one, and we can simply solve this equation for theta. So we can say that Seita is going to be equal to 1/2 time's arc sine of negative of rather of one. It's arc sine of one is going to be equal to pi over, too, and this is going to be times one over two. So Fada is going to be equal to pi over four. And of course, there are 180 degrees in every pie radiance, so this is going to equal 45 degrees. So that's why you get the maximum range when Seita equals 45 degrees, because you get the, ah maximum distance in the air. However, at the same time you're maximizing the amount of velocity in the ex direction. So again, the are max occurs when theta equals 45 degrees. That's the end of the solution. Thank you for watching.

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