An unsuspecting bird is coasting along in an easterly direction at 3.00 mph when

Question

An unsuspecting bird is coasting along in an easterly direction at 3.00 mph when a strong wind from the south imparts a constant acceleration of 0.400 m/s^2. If the acceleration from the wind lasts for 3.70 s, find the magnitude, r, and direction, ?, of the bird's displacement during this time period. (HINT: assume the bird is originally travelling in the +x direction and there are 1609 m in 1 mile.)

r=_______ meters
theta=________degrees

Now, assume the same bird is moving along again at 3.00 mph in an easterly direction but this time the acceleration given by the wind is at a 45.0 degree angle to the original direction of motion. If the magnitude of the acceleration is 0.200 m/s^2, find the displacement vector r, and the angle of the displacement, ?1. Enter the components of the vector and angle below. (Assume the time interval is still 3.70 s.)

r= _______meters i + _______meters j
?1=__________ degrees

Explanation / Answer

PART A Bird is coasting along in an easterly direction at 3.00 mph = 0.447 m/s Strong wind from the south imparts a constant acceleration of 0.400 m/s^2 Displacement towards East = 0.447*3.7= 1.654 m Displacement towards North = .5*0.4*3.7^2 = 2.738 m Magnitude of Displacement = Sqrt(1.654^2 + 2.738^2) = 3.2 m Direction WRT +x axis = 58.86 degrees. PART B Horizontal Displacement = 0.447*3.7 + 1.369 sin(45) = 2.622 m Vertical Displacement = 1.369 cos(45) = 0.968 m Angle= 20.26 degrees.

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