1) An airplane with a speed of 86.1 m/s is climbing upward at an angle of 31.5 ? with respect to the horizontal. When the plane's altitude is 805 m, the pilot releases a package. (a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the earth. (b) Relative to the ground, determine the angle of the velocity vector of the package just before impact.
The answer to part (a) is 1313.6m but I can't get the answer to (b).
2) In the javelin throw at a track-and-field event, the javelin is launched at a speed of 23.0 m/s at an angle of 31.6 ? 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 31.6 ? at launch to 16.0 ??
Any help with these two would be appreciated.
Thread: Reps for physics help
02-02-2009, 05:25 PM #1
Reps for physics help
02-02-2009, 05:32 PM #2
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the x component will be the same as the plane's x component of velocity.
the y component will have to be found using y= 1/2gt^2 since you know the height, you can use that to find time. then when you have time, you can use it to find the final velocity just before it hits the ground with the equation (v-final)^2= -2g(delta time)
so when you have the x and y components, then you can use trig to figure out the angle. x will be a positive x value and the y should be a -y value, so the angle should probably be in the range of 270-360 degrees, or 0-90 below the horizontal.
does that make sense?
02-02-2009, 05:34 PM #3
02-02-2009, 05:37 PM #4
02-02-2009, 09:20 PM #5
02-02-2009, 09:24 PM #6
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02-02-2009, 09:28 PM #7
02-02-2009, 09:46 PM #8
02-02-2009, 09:48 PM #9
02-02-2009, 09:52 PM #10
alright 2 is harder than i expected i think it can be solved using related rates though
edit: 2 is really easy
tan (theta) = y comp of velocity/ x comp of velocity
since you solved 1a ill assume you can resolve vectors, so resolve the inital situation you will get x comp = 19.58, y comp = 12.05
but the y comp changes by 9.8m/s^2, x comp stays the same obviously
so you have
tan(theta) = (12.05-9.8t)/(19.58)
plug in 16 for theta and solve for t
Last edited by skinnycalves; 02-02-2009 at 10:28 PM.
02-02-2009, 10:07 PM #11
02-02-2009, 10:18 PM #12
when the package is released its horizontal speed is that of the plane, which since you solved 1a, you know that x comp velocity = 73.41 m/s, imagine at that point in time hte package is being thrown from the cliff at 73.41 m/s (neglecting air resistance this should not change at all during the flight path), and its y comp velocity initial = 0 m/s but that is subject to an acceleration by gravity
distance in y direction=.5gt^2 (since velocity y initial is 0, dont even include it)
t= 12.8 seconds
the ball travels for 12.8 seconds before hitting the ground
so horizontal d = 73.41(t) = 73.41 (12.8) = 939.648 meters from release point
add that to 1313 from the takeoff point you get 2252.648 meters
02-02-2009, 10:26 PM #13