An airplane is flying at 500 km/hr at an angle of 310 degrees. The wind is blowing at 45 km/hr at an angle of 225 degrees. What is the resultant speed and direction of the plane?
We can set this up as two vectors, the first for the plane and the second for the wind...so we have
u = < 500cos310, 500sin310 > v = < 45cos225, 45sin225 >
Adding the x components, we have 500cos310 + 45cos225 = 289.57
Adding the y components, we have 500sin310 + 45sin225 = -414.84
The resultant is given by √(289.572 + (-414.84)2 ) = about 505.9 km'hr
The direction is given by tan-1(-414.84/289.57) = about (- 55.08) degrees = about 304.91 degrees
This makes sense......the wind is helping to increase the speed of the plane but it is also blowing it toward a more "southerly" direction.....
We can set this up as two vectors, the first for the plane and the second for the wind...so we have
u = < 500cos310, 500sin310 > v = < 45cos225, 45sin225 >
Adding the x components, we have 500cos310 + 45cos225 = 289.57
Adding the y components, we have 500sin310 + 45sin225 = -414.84
The resultant is given by √(289.572 + (-414.84)2 ) = about 505.9 km'hr
The direction is given by tan-1(-414.84/289.57) = about (- 55.08) degrees = about 304.91 degrees
This makes sense......the wind is helping to increase the speed of the plane but it is also blowing it toward a more "southerly" direction.....