Starting at the origin, you travel a distance 4.6 m in a direction 67.4 degrees

Question

Starting at the origin, you travel a distance 4.6 m in a direction 67.4 degrees north of east. Then, from this new postition, you travel another distance 1.6 m in a direction 32.7 degrees north of east.

a) In your final postition, how far are you from the origin? ___________m

b) In your final position, how many degrees north of east are you as measured from the origin? _____________degrees

c) Suppose that during both phases of your motion, you moved with a constant speed of 8.7 m/s. How much time does the whole trip take, from the origin to your final position? _______s

d) What is the magnitude of your average velocity for the whole trip from the origin to your final position? ____________m/s

e) What was the magnitude of your average acceleration for the whole trip from the origin to your final position? ______________m/s2

Explanation / Answer

let East be +x axis

A = 4.6 m

B = 1.6 m

Ax = 4.6*cos(67.4) = 1.77 m
Ay = 4.6*sin(67.4) = 4.25 m
Bx = 1.6*cos(32.7) = 1.35 m
By = 1.6*sin(32.7) = 0.86 m

a) Rx = Ax + Bx
=1.77+1.35=3.12m

Ry = Ay + By

=4.25+0.86 = 5.11

R = sqrt(Rx^2 + Ry^2)

= sqrt(3.12^2 + 5.11^2)

= 5.99 m

b) theta = tan^-1(Ry/Rx)

= tan^-1(5.11/3.12)

= 58.6o N of E

c) time taken = distance travelled/speed

= (4.6+1.6)/8.7

= 0.71s

d) Average velocity = displacement/time taken

= 5.99/0.71

= 8.4 m/s

e) ax = dvx/dt

= (8.7*cos(32.7) - 8.7*cos(67.4))/0.71

= 5.6 m/s^2

ay = dvy/dt

= (8.7*sin(32.7) - 8.7*sin(67.4))/.71

= -4.7 m/s^2

|a_avg| = sqrt(ax^2 + ay^2)

= 7.31 m/s^2

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