Find the resultant vector? 1/6 of 240 m/s directed east ?= 1/4 of 240 m/s 1/5 of 250 degrees south of west

1 Answer
May 30, 2018

Amplitude: # 45.98 m/s#

Direction: # 88.2^@# South of East

Explanation:

Because #240/6 = 40# ; #240/4 = 60# ; #250/5 = 50# the question can be translated to:
"Find the resultant vector? 40 m/s directed east + 60 m/s 50 degrees south of west" (I also assumed the question mark in the middle of the question was intended to indicate calculating the vector sum of the 2 velocities.)

Find components of the 2nd velocity in the East-West and North-South directions:

East-West #" "60 m/s*cos50 = 38.57 m/s "West"#
North-South #" "60 m/s*sin50 = 45.96 m/s "South"#

Since the first velocity is Eastward it can be combined with the East-West component of the 2nd given velocity. Since they are opposite directions, subtraction is required.

#40 - 38.57 m/s "East" = 1.43 m/s "East"#

So now we need to combine #1.43 m/s "East"# and #45.96 m/s "South"#. That calls for Pythagoras to find the magnitude and arctangent to find the direction.

Magnitude: #sqrt(1.43^2 + 45.96^2)" " m/s = 45.98 m/s#

Direction: #tan^-1(45.96/1.43) = 88.2^@# South of East

I hope this helps,
Steve