Starting at the origin, you travel a distance 3.1 m in a direction 51.7 degrees
ID: 1539688 • Letter: S
Question
Starting at the origin, you travel a distance 3.1 m in a direction 51.7 degrees north of east. Then, from this new postition, you travel another distance 4.1 m in a direction 44.6 degrees north of east.
a) In your final postition, how far are you from the origin? (answer in m)
b) In your final position, how many degrees north of east are you as measured from the origin? (answer in degrees)
c) Suppose that during both phases of your motion, you moved with a constant speed of 6.1 m/s. How much time does the whole trip take, from the origin to your final position? (answer in s)
d) What is the magnitude of your average velocity for the whole trip from the origin to your final position? (answer in m/s)
e) What was the magnitude of your average acceleration for the whole trip from the origin to your final position? Answer in m/s^2)
Explanation / Answer
let East be +x axis
A = 3.1 m
B = 4.1 m
Ax = 3.1*cos(51.7) = 1.92 m
Ay = 3.1*sin(51.7) = 2.42 m
Bx = 4.1*cos(44.6) = 2.92 m
By = 4.1*sin(44.6) = 2.88 m
a) Rx = Ax + Bx
= 1.92 + 2.92
= 4.84 m
Ry = Ay + By
= 2.42 + 2.88
= 5.3 m
R = sqrt(Rx^2 + Ry^2)
= sqrt(4.84^2 + 5.3^2)
= 7.18 m <<<<<<<<<<<<<<<<<<<<<------------Answer
b) theta = tan^-1(Ry/Rx)
= tan^-1(5.3/4.84)
= 47.6 North of East <<<<<<<<<<<<<<<<<<<<<------------Answer
c) time taken = distance travelled/speed
= (3.1 + 4.1)/6.1
= 1.18 s <<<<<<<<<<<-----------------Answer
d) Average velocity = displacement/time taken
= 7.18/1.18
= 6.08 m/s <<<<<<<<<<<-----------------Answer
e) ax = dvx/dt
= (6.1*cos(44.6) - 6.1*cos(51.7))/1.18
= 0.477 m/s^2
ay = dvx/dt
= (6.1*sin(44.6) - 6.1*sin(51.7))/1.18
= -0.427 m/s^2
|a_avg| = sqrt(ax^2 + ay^2)
= sqrt(0.477^2 + 0.427^2)
= 0.640 m/s^2 <<<<<<<<<<<<-----------------Answer
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