A particle undergoes two displacements The first has a magni

A particle undergoes two displacements. The
first has a magnitude of 11 m and makes an
angle of 76? with the positive x axis.
The result after the two displacements is
8.7 m directed at an angle of 109 ? to the
positive x axis using counter-clockwise as the
positive angular direction (see the figure be-
low).
Find the magnitude of the second displace-
ment. Answer in units of m.

Solution

The first displacement
.
delta x = 11 cos 76 = 2.661
delta y =11 sin 76 = 10.67
.
The final displacement
.
delta x = 8.7 cos 109 = -2.832
delta y = 8.7 sin 109 = 8.23
.
The second displacement
.
delta x = -2.832-2.661 = -5.493
delta y = 8.23 - 10.67 = -2.44
.
Magnitude of 2nd displacement = sqrt{ 5.493^2 +2.44^2 } = 6.01 m