A man leaves his front door, walks 330 m east and 320 m north, stopping at the edge of a cliff. He then takes a penny from his pocket and drops it from the cliff, which is 10 m high. What is the magnitude of the displacement (in meters) of the penny?
I'm confused on how a drawing of this would look and then how would you solve it. Would the vertical leg end up being 310 m and then you find the hypotenuse?
horizontal distance (not displacement vector)
hd= sqrt (330^2 + 320^2)
vertical distance
= 10
total distance = sqrt(hd^2+100)
the 330 and 320 form a right triangle
the hypotenuse is the horizontal displacement
the horizontal and vertical displacements also form a right triangle
since the three directions are orthogonal
... 330^2 + 320^2 + 10^2 = d^2
To visualize the situation described, you can draw a diagram:
Start with a point representing the man's front door. Label this as point A. From point A, draw a line segment 330 m long to the right (east). This represents the man's horizontal motion. At the end of this line segment, label the point as B.
From point B, draw a line segment 320 m long upwards (north). This represents the man's vertical motion. At the end of this line segment, label the point as C. Point C represents the position where the man stops, at the edge of the cliff.
Finally, from point C, draw a vertical line segment 10 m long downwards. This represents the height of the cliff. Label the bottom end of this line segment as D. Point D represents the point where the penny is dropped.
To find the magnitude of the displacement of the penny, you can think of it as the distance between points A and D. Notice that if you directly calculate the hypotenuse of the triangle formed by points A, B, and C, it doesn't take into account the vertical displacement caused by the height of the cliff. Therefore, you need to consider the vertical displacement of the penny as well.
You correctly stated that the vertical leg is 320 m. However, to find the magnitude of the displacement, you need to calculate the diagonal distance between points A and D.
To solve the problem, you can use the Pythagorean theorem, which states that for a right-angle triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse represents the displacement of the penny, the horizontal side represents the 330 m distance walked east, and the vertical side represents the 320 m distance walked north.
So, using the Pythagorean theorem, the magnitude of the displacement can be found as:
displacement² = (330²) + (320²)
Once you calculate the sum of the squares, you can take the square root of the result to find the magnitude of the displacement of the penny.