A pilot wants to fly west. If the plane has an airspeed of 95 m/s and there is a 25 m/s wind blowing north:
A. In what direction must she head the plane?
B. What will be her speed relative to the ground?
C. How far will the plane go in 2.25 h?
Can you explain how I would do this?
Head T degrees south of west
then
95 sin T = 25
sin T = .263
T = 15.25 degrees south of west
now
total speed north over ground = 0
Vw = total speed west over ground = 95 cos 15.25 m/s
so in 2.25 hr distance = 2.25 * Vw
All angles are measured CW from +y-axis.
A. Vr = Vp + 25i = 95m/s[270o] = Resultant velocity,
Vp + 25i = 95*sin270 + (95*Cos270)I,
Vp + 25i = -95 + 0i,
Vp = -95 - 25i = 98m/s[75o] W. of S. = 255o CW.
Direction = 75o W. of S. = 15o S. of W. = 255o CW.
B. Speed = 98 m/s(Part A.).
C. d = Vr * T = 95 * 2.25 = ___m.
Sure! To solve this problem, you need to use vector addition and some trigonometry.
A. To determine the direction the pilot must head the plane, you need to consider the effect of the wind on the plane's movement. In this case, the wind is blowing north, which means it has a velocity of 25 m/s in the y-direction (positive direction). The plane's airspeed is 95 m/s to the west, which means it has a velocity of 95 m/s in the x-direction (negative direction).
To find the resultant velocity (the velocity of the plane relative to the ground), you need to add the velocities of the plane and wind using vector addition. The direction of the resultant velocity will be the direction the pilot must head the plane.
B. The speed of the plane relative to the ground can be determined by finding the magnitude of the resultant velocity.
C. To find how far the plane will go in 2.25 hours, you can calculate the displacement using the formula:
Displacement = Velocity * Time
Now, let's solve each part step by step:
A. To find the direction the pilot must head the plane, you can use the trigonometric concept of finding the angle with respect to the x-axis. The angle can be found using the tangent function:
Angle = arctan(Vy / Vx)
where Vy is the velocity of the wind in the y-direction (25 m/s) and Vx is the velocity of the plane in the x-direction (-95 m/s).
B. To find the speed of the plane relative to the ground, you need to find the magnitude of the resultant velocity. This can be found using the Pythagorean theorem:
Resultant velocity = √(Vx^2 + Vy^2)
where Vx is the velocity of the plane in the x-direction (-95 m/s) and Vy is the velocity of the wind in the y-direction (25 m/s).
C. To find the displacement of the plane in 2.25 hours, you can multiply the velocity by the time:
Displacement = Resultant velocity * Time
where Resultant velocity is the magnitude of the resultant velocity calculated in part B, and Time is 2.25 hours.
I hope this explanation helps! If you have further questions, feel free to ask.