please explain steps taken. Question 8 of 13 An unsuspecting bird is coasting al

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please explain steps taken.

Question 8 of 13 An unsuspecting bird is coasting along in an easterty direction at 3.00 mph when a strong wind from the south imparts a constant acceleration of 0.400 m/s2. If the wind's acceleration lasts for 3.60 s, find the magnitude r and direction (measured counterdockwse from the easterly direction) of the bird's displacement over this time interval. (HINT: assume the bird is originally t ravelling in the +x direction and there are 1609 m in 1 mile.) Number Number acceleration given by the wind is at a 32.0 degree angle to the original direction of motion. it the magnitude of the acceleration is 0.200 mis2 find the displacement vector Enter the components of the vector and angle below (Assume the time interval is stil 3.60 s) and the angle of the displacement, 9n Number Number 113 Tools Number Chtch Answer 0 NuxlEnt- previous

Explanation / Answer

+i = +x = East

+j = +y = North

Part 1)

vi = 3.00 mph East = 3.00i + 0j mph

Convert mph to m/s

vi = (3.00i + 0j) mph * (1609 m / 1 mile) * ( 1 hr / 3600 s) = 1.34i + 0j m/s

a = 0.400 m/s^2 FROM THE SOUTH = 0.400 m/s^2 North = 0i + 0.400j m/s^2

Equation of motion:

sf = si + vi*t + 1/2*a*t^2

Assume si = 0

sf = vi*t + 1/2*a*t^2

sf = (1.34i + 0j m/s)*3.60 s + 1/2 * (0i + 0.400j m/s^2) * (3.60 s)^2

sf = (4.824i + 0j m) + (0+2.59j m)

sf = (4.824+0)i + (0+2.59)j m

sf = 4.824i + 2.59j m

So, after 3.6 s, the birds displacement from the start is 4.824m in the East direction and 2.59m in the North direction. You have the two legs of the triangle now.

||sf|| = sqrt(4.824^2 + 2.59^2) m = 5.48 m

direction = atan(j/i) = 28.2 deg Cartesian or 28.2 deg North of East or 61.8 deg Compass

Part 2)

vi = 1.34i + 0j m/s

a = 0.200 m/s^2 32.0 deg above/below East (x-axis, i-axis) = 0.200 m/s^2 * (cos(32.0)i + sin(32.0)j) = 0.17i + 0.106j m/s^2

Again, sf = vi*t + 1/2*a*t^2

sf = (1.34i + 0j m/s) * (3.60 s) + 1/2 * (0.17i + 0.106j m/s^2) * (3.60 s)^2

sf = (4.824i + 0j m) + (1.1i + 0.687j m)

sf = 5.924i + 0.687j m

||sf|| = sqrt(5.924^2 + 0.687^2) m = 5.96 m

angle = atan(j/i) = 6.61 deg Cartesian or 6.61 deg North of East or 83.4 deg Compass

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