A: a man travels 7.0km due north then 10.0km east. Find the
resultant displacement
sqrt(49+100) = sqrt 149 = 12.2 km
angle east of north = tan^-1 (10/7)
so 55 degrees east of north
or in x y coordinates (90-55) = 35 degrees above x axis
Hint: Set up a diagram, use Pythagorean Theorem, and then use inverse tangent to find the angle. Tell us what you get from here.
To find the resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the man's travel in a north-south direction as one side of the triangle and the travel in an east-west direction as the other side. Therefore, the resultant displacement is the hypotenuse of the right triangle.
Using the given information, the man traveled 7.0 km due north and then 10.0 km east. This forms a right triangle. We can label the side opposite the angle formed by the north direction as the vertical side ("north-south side") and the side opposite the angle formed by the east direction as the horizontal side ("east-west side").
The vertical side has a length of 7.0 km, and the horizontal side has a length of 10.0 km.
Using the Pythagorean theorem, we can find the length of the resultant displacement (the hypotenuse):
Resultant displacement^2 = (north-south side)^2 + (east-west side)^2
Resultant displacement^2 = 7.0 km^2 + 10.0 km^2
Resultant displacement^2 = 49 km^2 + 100 km^2
Resultant displacement^2 = 149 km^2
Taking the square root of both sides to find the length of the resultant displacement:
Resultant displacement = √(149 km^2)
Calculating the square root of 149 km^2, we find:
Resultant displacement ≈ 12.21 km
Therefore, the resultant displacement is approximately 12.21 km.