Vector Addition Problems?

Question

Indiana Jones is trapped in a maze. To find his way out, he walks 10.0m, makes a 90.0 degrees right turn, walks 5.00m, makes another 90.0 degree right turn, and walks 7.00m. What is his displacement from his initial position?

Answer 1

Draw a right triangle and and measure the hypotenuse.

Answer 2

Actually draw the three lines and THEN draw a right triangle. Since the 10 and the 7 are parallel, one of the sides of the triangle is 10 - 7 or 3. The other is the 5 meters. The displacement is then:

D = SQRT(3^2 + 5^2) = SQRT(34)

Answer 3

Firstly, u have to draw a free-body diagram.
Assume she is trapped at the origin, x=0, y=0.

Then he walks 10.0 m along the positive x-axis (rightward). when she makes 90 degrees right turn means she walks along negative y-axis (downward) for 5.0 m. She again turns 90 degree, means along negative x-axis (to the left) with magnitude of 7.0 m.

then, u should separate the x and y component.

For her first walk:
x-component : 10 cos 0 = 10
y-comp : 10 sin 0 =0

For the second walk :
x-comp : -5 sin 0 = 0
y-comp : -5 cos 0 = -5

For the last :
x-comp : -7 cos 0 = -7
y-comp : -7 sin 0 = 0

Make x and y component summation, separately.
Sum of x-comp = 3
sum of y-comp = -5

To find the resultant displacement, R,

R = [ (3)^2 + (-5)^2 ] ^ (1/2)

^ means the power of.

Hence, the displacement is = (34) ^ (1/2)
or
the square root of 34.

Answer 4

You need to draw this:

You will need to use trigonometry too.

So assuming you drew the problem you will need to find the displacement which is the distance from point A to the last point (C in this case).

So the equation for this is:

displacement= sqrt(5^2+(10-7)^2)
displacement =5.83095

Your displacement is approximately 5.83m

Answer 5

let's call the 10 m initial direction the Y direction, the 5 m direction the X direction

In effect he went +3 m in the Y and + 5 m in x direction.

His distance is (3^2 + 5 ^2)^0.5 or 6 meters

His angle from initial position is arctan (3/5) = 31 degress in the + y direction

Answer 6

The answer is square root of 34. Draw the sketches. and find out