L5_phys131_28sep07

L5_phys131_28sep07 - launch speed is 4.0 m/s When projected...

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A Grumman AA5B/G single-engine airplane in still air has a ground speed of 160 MPH. Bill wants to fly due east, but is facing a fierce 50 MPH headwind directed 40 0 south of west, as shown below. A) At what angle θ should he point his plane so that it ends up traveling due east? B) What will be his ground speed? θ 40 0 50 MPH wind 160 MPH plane W N E S
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Solutions to plane problem: 160 MPH v GROUND θ 50 MPH 40 0 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 MPH 118 v 40 cos MPH 50 6 . 11 cos MPH 160 V 6 . 11 MPH 160 40 sin MPH 50 sin 0 40 sin MPH 50 sin MPH 160 GROUND 0 0 GROUND 0 0 1 0 = - = = = θ = - θ -
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2D and 3D kinematics with components k ˆ a j ˆ a i ˆ a a k ˆ v j ˆ v i ˆ v k ˆ dt dz j ˆ dt dy i ˆ dt dx dt r d v k ˆ z j ˆ y i ˆ x r z y x z y x + + = + + = + + = = + + = While the vector acceleration is constant in magnitude and direction, what happens in one coordinate is independent of what happens in another.
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By shooting vertically, your group has determined that a ball’s initial
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Unformatted text preview: launch speed is 4.0 m/s. When projected off a table at an angle of 40 0 above horizontal, what is the horizontal distance L that the ball will travel before it lands on the floor? The floor is 1.0 meter below the ball’s launch point. This is similar to this week’s lab, but there are subtleties. For example, in the lab the ball will be launched slightly above table height. L 1 m 40 Solution to ball shooting problem ( 29 [ ] ( 29 ( 29 [ ] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 ( 29 m 41 . 2 s 785 . 766 . s / m 4 t cos v L s 785 . 2 2041 . 4 5247 . 5247 . t 2041 . t 5247 . t t s / m 8 . 9 2 1 t 40 sin s / m 4 m 1 t g 2 1 t sin v h 2 2 2 2 2 = = θ = = + + = =---=--θ =-...
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