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 0.200 m/s2. If the acceleration from the wind lasts for 3.90 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=

?=

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 32.0 degree angle to the original direction of motion. If the magnitude of the acceleration is 0.400 m/s2, find the displacement vector , and the angle of the displacement, ?1. Enter the components of the vector and angle below. (Assume the time interval is still 3.90 s.)

r=

^i=

?=

Explanation / Answer

ax = 0 .....ay = 0.2

v = 3mph = 3*(1609/3600) = 1.34 m/s

x = vx*t + 0.5*ax*t^2 = 1.34*3.9 = 5.226 m

y = Vy*t + 0.5*ay*t^2 = 0 + (0.5*0.2*3.9*3.9) = 1.521 m

r = 5.226 i + 1.521 j

theta = 16.22

-----------------

ax = 0.4*cos32 = 0.34 .....ay = 0.21 m/s^2

v = 3mph = 3*(1609/3600) = 1.34 m/s

x = vx*t + 0.5*ax*t^2 = (1.34*3.9)+(0.5*0.34*3.9*3.9) = 7.8117 m

y = Vy*t + 0.5*ay*t^2 = 0 + (0.5*0.21*3.9*3.9) = 1.59705 m

r = 7.8117 i + 1.59705 j

theta = 11.55

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