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

In summary, the author calculated the vertical and horizontal velocity components of a resultant velocity of 240 m/s. They then used the vertical component, the given vertical distance, and gravity to calculate the time needed for the object to fall to the ground.
  • #1
deserthobo
13
0

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?
 
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  • #2
you want the arc tan of the final velocities Vyf/Vxf
 
  • #3
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
 
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  • #4
denverdoc, I think deserthobo is right is the arctan of distances, the 2.4 km and the horizontal range of the flare.
 
  • #5
hmm...the time needed for the object to fallwell, vf = vo + at

vf = 0 so...
 
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  • #6
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.
 
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  • #7
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?
 
  • #8
ok, t is not just 12, there are some extra digits as well (i'm horrible with sig digs as well :-p)

also, the horizontal velocity is constant

and velocity = distance/time

so, distance = velocity * time

you know the time, and you know the velocity
 
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  • #9
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!
 
  • #10
deserthobo said:
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.
 
  • #11
Are you a doctor? :)
 
  • #12
guilty as charged, tho a psychiatrist in the minds of many of his fellow physicians has lost any valid claim to the title
 

1. What is a "2 dimen kinematics problem"?

A "2 dimen kinematics problem" refers to a physics problem that involves analyzing the motion of an object in two dimensions, typically on a flat surface. This includes the object's position, velocity, and acceleration in both the x and y directions.

2. How do you solve a 2 dimen kinematics problem?

To solve a 2 dimen kinematics problem, you first need to identify and label the variables given in the problem, such as initial and final positions, velocities, and accelerations. Then, you can use equations such as the kinematic equations or vector equations to calculate the unknown variables.

3. What are the key differences between 1 dimen and 2 dimen kinematics problems?

The main difference between 1 dimen and 2 dimen kinematics problems is the number of dimensions involved. In 1 dimen problems, the motion of an object is only analyzed in one direction (typically the x direction), while in 2 dimen problems, the motion is analyzed in both the x and y directions. This requires considering vector components and using vector equations in addition to the kinematic equations.

4. What are some common types of 2 dimen kinematics problems?

Some common types of 2 dimen kinematics problems include projectile motion, circular motion, and motion on an inclined plane. Projectile motion involves an object being launched at an angle and moving in a curved path, while circular motion involves an object moving in a circular path with a constant speed. Motion on an inclined plane involves an object moving up or down a sloped surface.

5. How can I check if my answer to a 2 dimen kinematics problem is correct?

To check if your answer is correct, you can plug the values back into the original problem and see if they satisfy all the given conditions. You can also use the equations of motion to calculate the object's position, velocity, and acceleration at different time intervals and compare them to your calculated values. Additionally, you can use diagrams or graphs to visually represent the motion and check if your calculated results match the expected pattern.

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