An unsuspecting bird is coasting along in an easterly direction at 2.00 mph when

Question

An unsuspecting bird is coasting along in an easterly direction at 2.00 mph when a strong wind from the Map south imparts a constant acceleration of 0.200 m/s*. If the wind's acceleration lasts for 3.00 s, find the magnitude r and direction (measured counterclockwise from the easterly direction) of the bird's displacement over this time interval. (HINT: assume the bird is originally travelling in the +x direction and there are 1609 m in 1 mile.) Number r2.69 Im Number 9 27.54 Now, assume the same bird is moving along again at 2.00 mph in an easterly direction but this time the acceleration given by the wind is at a 42.0 degree angle to the original direction of motion. If the magnitude of the acceleration is 0.200 m/s, 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 3.00 s.) Number Number 1.8 mi88 Number '= | | 26.67 Previous Check Answer

Explanation / Answer

2.00 mph = 0.89408 m/s

the displacement after 3s is
r = 0.89408m/s*3s i + ½*0.200m/s²*(3s)² j = [2.68 i + 0.9 j] m
where "i" and "j" are the unit vectors "east" and "north," respectively

magnitude |r| = (2.68² + 0.9²) m = 2.83 m
direction = arctan(0.9 / 2.68) = 18.56º North of East

Now,
r = [(0.89408*3 + ½*0.200*cos42*3²) i + ½*0.200*sin42*3² j] m
r = [3.35 i + 0.602 j] m
1 = arctan(0.6022/3.35) = 10.2º

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