A spy stands on the sidewalk by an apartment building examining a foreign embassy across the street. The spy then climbs 30 m to the top the building and then slides 40 m along a wire at a 20° angle below right to reach a window on the embassy. What is their total displacement from the sidewalk to the embassy window?
the resultant i got qas 113.229, did anyone else get this?
after the spy climbs up i im not sure which way the spy goes down, i made him go south east (20 South of East) is this correct?
vertical distance along the wire:
h/40 = sin20°
h = 13.68
width of street:
w/40 = cos20°
w = 37.59
distance from sidewalk to window:
d^2 = w^2+(30-h)^2
= 37.59^2 + (30-13.68)^2
= 1679.35
d = 40.98
Not sure how you got such a large number. The wire was only 40, so the street has to be less than that.
He climbed up 30 and slid down, so he has to be at less than 30 upwards.
Given maximum values he'd only be √(30^2+40^2) = 50 from the window.
yea i was thinking that too,
To find the total displacement of the spy from the sidewalk to the embassy window, we can break down the different components of their motion.
First, the spy climbs 30 m vertically from the sidewalk to the top of the building. This vertical displacement can be represented as +30 m.
Next, the spy slides 40 m along a wire at a 20° angle below the right. To determine the horizontal and vertical components of this displacement, we need to use trigonometry.
The horizontal displacement (x-component) can be calculated using the cosine function:
Cos(20°) = Adjacent/Hypotenuse
Cos(20°) = x/40
x = 40 * Cos(20°)
The vertical displacement (y-component) can be calculated using the sine function:
Sin(20°) = Opposite/Hypotenuse
Sin(20°) = y/40
y = 40 * Sin(20°)
Since the spy is sliding at an angle below the right, we can determine the direction of the displacement using the relative position of the angles. In this case, 20° below the right means the direction is slightly south of east.
Therefore, the horizontal displacement (x-component) is +40 * Cos(20°) and the vertical displacement (y-component) is +40 * Sin(20°) in a slightly south-of-east direction.
Finally, we can find the total displacement by summing up the separate components of displacement:
Total displacement = Vertical displacement + Horizontal displacement + Initial vertical displacement
Total displacement = (40 * Sin(20°) + 30)i + (40 * Cos(20°))j
Evaluating this expression using the given values for sine and cosine, we get the total displacement of the spy from the sidewalk to the embassy window.