Use scale drawing method:
If a man travels 7km 30degree east of north,then 1okm east,find the resultant displacement
Did you make your sketch?
I see a triangle where I can use the cosine law, and
R^2 = 7^2 + 1^1 - 2(7)(1)cos120°
= 50 - 14(-.5)
= 50+7 = 57
R = √57
by sine law:
sinØ/1 = sin120/√57
Ø = 6.586
direction = 6.586+30 = N 36.586°E
or
using vectors:
vector r = (7cos60,7sin60) + (cos0, sin0)
= (7/2 , 7√3/2) + (1,0)
= (9/2 , 7√3/2)
|r| = √(81/4 + 147/4) = √57
direction : tan^-1 β = (7√3/2) / (9/2)
β = 53.413° or N 36.586°E
north distance = N = 7 cos 30
east distance = E = 1o (? assume 10) + 7 sin 30
magnitude of displacement = sqrt (N^2 + E^2)
angle east of north = tan^-1 (E/N)
To find the resultant displacement using the scale drawing method, we need to follow these steps:
1. Choose a scale for your diagram. For example, let's say we use a scale of 1 cm = 1 km.
2. Start by drawing a horizontal line to act as a reference point or baseline. This will represent the east direction.
3. Then, draw a line at a 30-degree angle to the north direction from the endpoint of the baseline. This line will represent the 7 km east of north direction.
4. Now, draw a line from the endpoint of the previous line parallel to the baseline, representing the additional 10 km east.
5. Measure the length of the resultant line from the starting point of the baseline to the endpoint of the last line. Remember, each centimeter on the diagram represents 1 km.
6. Based on the scale, determine the actual length of the resultant line. For example, if the measured length on the diagram is 5 cm, then the actual length is 5 km.
Therefore, the resultant displacement is 5 km.