MTALHAHASSAN2
  • MTALHAHASSAN2
Need help A duck flies 10 m [N20E] and then 5m due East. What is the displacement of the duck?
Physics
schrodinger
  • schrodinger
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anonymous
  • anonymous
displacement will be the sum of the two vectors. Can you resolve the 10 m vector? |dw:1435792790703:dw|
anonymous
  • anonymous
\[r_1=10\cos70° i+ 10 \sin 70° j\] \[r_2=5\cos0°i+5\cos0°j = 5 i\]
MTALHAHASSAN2
  • MTALHAHASSAN2
ok

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MTALHAHASSAN2
  • MTALHAHASSAN2
wait but how can we find the displacement
MTALHAHASSAN2
  • MTALHAHASSAN2
anonymous
  • anonymous
add the vectors d = (5+10 cos 70°)i + (10 sin 70°)j d = 8.42 i + 9.40 j Now just find the magnitude (√(x² + y²)) and direction (arctan (y/x))
MTALHAHASSAN2
  • MTALHAHASSAN2
how you get sin and cos 70
MTALHAHASSAN2
  • MTALHAHASSAN2
is it 90-20
anonymous
  • anonymous
yes. I just like working with the angle to the horizontal. You can also make the x be 10 sin 20 and then y would be 10 cos 20. You get the same results
MTALHAHASSAN2
  • MTALHAHASSAN2
I get 12.6
anonymous
  • anonymous
yes 12.6 m. the direction is arctan (9.4/8.42) = 48.14° from the horizontal which is 90-48.14 = 41.85° from the vertical So the displacement is about 12.6 m N42E

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