MTALHAHASSAN2 one year ago Need help A duck flies 10 m [N20E] and then 5m due East. What is the displacement of the duck?

1. anonymous

displacement will be the sum of the two vectors. Can you resolve the 10 m vector? |dw:1435792790703:dw|

2. anonymous

$r_1=10\cos70° i+ 10 \sin 70° j$ $r_2=5\cos0°i+5\cos0°j = 5 i$

3. MTALHAHASSAN2

ok

4. MTALHAHASSAN2

wait but how can we find the displacement

5. MTALHAHASSAN2

@peachpi

6. 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))

7. MTALHAHASSAN2

how you get sin and cos 70

8. MTALHAHASSAN2

is it 90-20

9. 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

10. MTALHAHASSAN2

I get 12.6

11. 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