HELP second parts not right An unsuspecting bird is coasting along in an easterl

Question

HELP second parts not right

An unsuspecting bird is coasting along in an easterly direction at 1.00 mph when a strong south imparts a constant acceleration of 0.400 m/s2. If the acceleration from the wind lasts Tor 2.20 s, find the magnitude, r, and direction, theta, 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.) 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 46.0 degree angle to the original direction of motion. If the magnitude of the acceleration is 0.500 m/s2, find the displacement vector , and the angle of the displacement, theta1. Enter the components of the vector and angle below. (Assume the time interval is still 2.20 s.)

Explanation / Answer

initially u = 1mph = 1 x1609 / 3600 = 0.447 m/s

so velocity vector v = 0.447 i m/s

acceleration given by wind = 0.5 m/s2   ....at an angle of 46 degree

so acce. vector a = 0.5cos46i + 0.5sin46j   m/s2

so displacement vector :

r = (v_xt + a_xt^2/2)i + (v_y t + a_y t^2/2)j

= (0.447 x 2.20 + 0.5cos46 x 2.20^2/2)i   + (0 + 0.5sin46 x 2.20^2/2)j

= 1.82i + 0.870j m ............................ANs

angle   = tan-1(-0.870 / 1.82) = 25.55 degrees

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