An unsuspecting bird is coasting along in an easterly direction at 1.00 mph when

Question

An unsuspecting bird is coasting along in an easterly direction at 1.00 mph when a strong wind from the Map ADA south imparts a constant acceleration of 0.200 m/s2. If the wind's acceleration lasts for 3. 10 s, find the magnitude rand direction a (measured counterclockwise from the easterly direction) of the bird's displacement over this time interval. (HINTassume the bird is originally travelling in the +x direction and there are 1609 m in 1 mile.) Number r= 5.87 m Number 0 = 19.08 Now, assume the same bird is moving along again at 1.00 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 0.400 m/s2, find the displacement vector r, and the angle of the displacement, e. Enter the components of the vector and angle below. (Assume the time interval is still 3.10 s.) Number Number ., mi + 1.05 Number 8.37 G Previous O Check Answer Next > Exit I Hint

Explanation / Answer

1) displacement in x = vt = 1*3.1 mile = 3.1* miles

= 4988 m

displacement in y = 0.5at^2 = 0.5*0.2*3.1^2

= 0.961 mile = 1546 m

r = sqrt (4988^2 +1546^2)

= 5222 m

theta = arctan (1546/4988)

= 17.22 degree

2) displacement in x = 1*3.1+ 0.5*0.4 cos 42 degree*3.1^2

= 4.53 mile = 7289 m

Displacement in y = 0.5*0.4*sin 42 degree *3.1^2

= 1.286 mile = 2069 m

R = 7289 i + 2069 j

Theta = arctan (2069/7289) = 15.85 degree

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