PhysicsASAP
posted by Fizza .
A plane has an airspeed of 200 {mph}. The pilot wishes to reach a destination 600 {mi} due east, but a wind is blowing at 50 {mph} in the direction 30 degrees north of east.
a)In what direction must the pilot head the plane in order to reach her destination? answer in south of east
b)How long will the trip take?
answer in hours
can you please show me step by step so i can check my answer?
thanks

PhysicsASAP 
Steve
You want two vectors which add up to (0,600). The airspeed has length 200t in an unknown direction, angle a. The other has length 50t, in the direction 30º north of east.
So, if the destination D = (600,0)
P is the point where the plane would have ended up with no crosswind.
P = (x,y) where
y = 25t because of the 30º angle.
So, now we have two right triangles.
On the left, the hypotenuse = 200t, height = 25t, base = 25t√63
On the right, hypotenuse=50t, height=25t, base=25t√3
Now, we know that the two bases add up to 600mi.
25t(√63+√3) = 600
t = 2.48 hrs
Using the plane's triangle, sin(a) = 1/8
a = 7.18º south of east.
You can use the law of cosines to verify that the numbers are correct.
Respond to this Question
Similar Questions

precal
a pilot wants to fly on a bearing of 66.4 degrees. by flying due east, he finds that a 57mph wind, blowing from the south, puts him on course. Find the airspeed of the plane. Sketch this. He flys east unknown speed. The plane goes … 
word problem
An airplane is flying with a heading of 60 degrees east of north at 450 mph. A wind is blowing at 37 mph from the north. Find the plane's ground speed to the nearest mph and direction to the nearest degree. Thanks. 
Physics
a plane has an airspeed of 200 mph. the pilot wants to reach a destination 600 miles east but a wind is blowing 50 mph 30 degrees North of East. What direction must the pilot head the plane in order to reach the destination? 
calculus III
What heading (or direction) and airspeed (speed in still air) are required for an airplane to fly 837 mph due north if a wind of 63 mph is blowing in the direction of S 11.5 degrees E? 
calculus iii
What heading (or direction) and airspeed (speed in still air) are required for an airplane to fly 837 mph due north if a wind of 63 mph is blowing in the direction of S 11.5 degrees E? 
Physics
A plane is heading due south with an airspeed of 211 mph. A wind from a direction of 53 degrees is blowing at 17 mph. Find the bearing of the plane. (Note that bearings are measured from north, clockwise.) Round results to appropriate … 
Physics
A light plane attains an airspeed of 491 km/h. The pilot sets out for a destination 785 km due north but discovers that the plane must be headed 20.5° east of due north to fly there directly. The plane arrives in 2.25 h. What was … 
Math
An airplane is going 300 mph at a bearing of N 55 degrees E. The wind is blowing 30 mph due East. What is the actual speed and direction of the plane? 
physics
The pilot of an airplane wishes to fly due north, but there is a 71 km/h wind blowing toward the east. (a) In what direction should the pilot head her plane if its speed relative to the air is 314 km/h? 
Physics
An airplane traveling at 200 mph in a direction of 40 degrees north of east encounters a wind blowing east at 50.0 mph. Find the velocity of the plane measured from the ground.