2D Vector problems

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• Sep 4th 2007, 03:17 AM
sir nerdalot
2D Vector problems
Hi,

i've got a bit stuck with this 2D vector problem!!
A Car is traveling at 60km/h on a bearing of 078 degrees T. Within the closed car a bee flies at 3m/s diagonally from the rear to the front corner so that its angle of flight is at 37 degrees with the axis of the car. Find the velocity that the bee is flying relative to the ground. Answer to 1 decimal place and bearing to nearest minute.
Thank you
• Sep 4th 2007, 04:47 AM
ticbol
If I understand your question, here is the solution.

The velocity of the car is 60 kph, at (90 -78) = 12 degrees above the East-axis.
The velocity of the bee in the car is 3m/sec, at (12 +37) = 49deg above the East-axis.

Km/h and m/sec. :)
Let use km/h all.

3m/sec *(1km /1000m)(3600sec /1hr) = 3*3600/1000 = 10.8 kph

So, Easting-components of the two velocities,
E = 60cos(12deg) +10.8cos(49deg) = 65.774 kph

Northing-components of the two velocities,
N = 60sin(12deg) +10.8sin(49deg) = 20.626 kph

Resultant of E and N,
R = sqrt[E^2 +N^2]
R = sqrt[(65.774)^2 +(20.626)^2] = 68.932 kph ---------***

Bearing, based from North,
tan(theta) = E/N = 65.774 /20.626 = 3.18888
theta = arctan(3.18888) = 72.589 degrees = 72deg and 35.34min --------***

Therefore, relative to the ground, the bee flies at the rate of 68.9 km/h on a bearing of 72deg,35min. ----------------answer.