What is the correct angle for the given 2D kinematics problem?

[deserthobo]

Homework Statement

http://img413.imageshack.us/img413/2919/physicsprobpr6.jpg

Xy=2400 m

Homework Equations

Xy=Voyt + 1/2at^2
Xx=1/2(Vox+Vx)t

The Attempt at a Solution

I calculated the vertical and horizontal velocity components of the given resultant velocity of 240 m/s.

Voy = 120 m/s
Vox = 208 m/s

then i used the vertical component, the given vertical distance and gravity to calculate the time needed for the package to fall to the ground.

t = 38 s

then i plugged this into Xx=1/2(Vox+Vx)t to find the horizontal distance the package travelled.

Xx= 3904

then i plugged this in with the given vertical distance into tan -1 (y/x) to get an angle of 31 degrees. but the book says 42 degrees! where did i go wrong guys?

 

[denverdoc]

you want the arc tan of the final velocities Vyf/Vxf

 

[deserthobo]

hmm why do i want the arc tan of the final velocities and not the arc tan of the distances?

also, arent the final velocites both = 0 since the package hits the ground

 

[Gyroscope]

denverdoc, I think deserthobo is right is the arctan of distances, the 2.4 km and the horizontal range of the flare.

 

[mybsaccownt]

hmm...the time needed for the object to fallwell, vf = vo + at

vf = 0 so...

 

[deserthobo]

ok using vf=vo + at i got 12 s

i plugged 12 s into x = 1/2(vf + vo)t and then found the arc tan with that number and came up with 62 degrees. doesn't work out.

 

[deserthobo]

ok guys, if i plug in the horizontal velocity component which is 208 for

vf and vo

for

x=1/2(vf+vo)t

i will get 2704 m, which when plugged into arc tan (y/x) will give me the angle of 41..5 which when rounded up is 42 degrees. but does it make sense to plug in 208 for both vf and vo?

 

[mybsaccownt]

ok, t is not just 12, there are some extra digits as well (i'm horrible with sig digs as well )

also, the horizontal velocity is constant

and velocity = distance/time

so, distance = velocity * time

you know the time, and you know the velocity

 

[deserthobo]

ok so i did everything following what mybsaccownt said and in the end i came up with 43 degrees. the book says 42 so this method is incorrect!

 

[denverdoc]

ok so i did everything following what mybsaccownt said and in the end i came up with 43 degrees. the book says 42 so this method is incorrect!

I think you and the book are likely bothright, round off error. And i was all wet, in a hurry between patients , and shouldn't have posted.

 

[Gyroscope]

Are you a doctor? :)

 

[denverdoc]

guilty as charged, tho a psychiatrist in the minds of many of his fellow physicians has lost any valid claim to the title