A radar device detects a rocket approaching directly from...

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Steebly
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Homework Statement


A radar device detects a rocket approaching directly from east due west. At one instant, the rocket was observed 10 km away and making an angle of 30 degrees above the horizon. At another instant the rocket was observed at an angle of 150 degrees in the vertical east-west plane while the rocket was 8 km away. Find displacement of the rocket during the period of observation.

Homework Equations

The Attempt at a Solution


I split each vector into subvector components by using equation Ax=A*cos(Theta) and Ay=A*sin(Theta). So Ax=10*cos(30) and Ay=10*sin(30). Bx=8*cos(150) and By=8*sin(150). Then I added Ax+Bx which equaled 1.74 and Ay+By which equaled 9. So Rx=1.74 and Ry=9. I then took sqrt( (1.74)^2+(9)^2) to fnd magnitude of R. I got 9.166 as the answer. So this is the displacement vector right? The book gives a value of 15.62 km but I got 9.166 km? What did I do wrong?
 
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Steebly said:

Homework Statement


A radar device detects a rocket approaching directly from east due west. At one instant, the rocket was observed 10 km away and making an angle of 30 degrees above the horizon. At another instant the rocket was observed at an angle of 150 degrees in the vertical east-west plane while the rocket was 8 km away. Find displacement of the rocket during the period of observation.

Homework Equations

The Attempt at a Solution


I split each vector into subvector components by using equation Ax=A*cos(Theta) and Ay=A*sin(Theta). So Ax=10*cos(30) and Ay=10*sin(30). Bx=8*cos(150) and By=8*sin(150). Then I added Ax+Bx which equaled 1.74 and Ay+By which equaled 9. So Rx=1.74 and Ry=9. I then took sqrt( (1.74)^2+(9)^2) to fnd magnitude of R. I got 9.166 as the answer. So this is the displacement vector right? The book gives a value of 15.62 km but I got 9.166 km? What did I do wrong?
Lay out the two vectors on some graph paper or make a plot with your computer.

You added the two vectors together, which doesn't produce the displacement of the rocket between A and B.
 
So I was suppose to subtract the vector components. I should have said Ax-Bx=Rx and Ay-By=Ry. Thank you very much