A man leaves his front door, walks 440 m east and 380 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 20 m high. What is the magnitude of the displacement (in meters) of the penny?
pennydisplacement: 440E + 380N + 20 down
magnitude: sqrt(440^2+380^2+20^2)
To find the magnitude of the displacement of the penny, we can use the Pythagorean theorem.
First, let's calculate the distance the man walked before reaching the cliff. He walked 440 m east and 380 m north, forming a right-angled triangle.
To find the distance, we can use the Pythagorean theorem:
distance = √(east^2 + north^2)
distance = √(440^2 + 380^2)
distance = √(193,600 + 144,400)
distance = √(338,000)
distance ≈ 581.23 m
So, the man walked approximately 581.23 m before reaching the cliff.
Next, we need to consider the height of the cliff. The penny is dropped from a 20 m high cliff.
Now, let's find the magnitude of the displacement of the penny.
Again, we can use the Pythagorean theorem to calculate the displacement:
displacement = √(distance^2 + height^2)
displacement = √(581.23^2 + 20^2)
displacement = √(338,000 + 400)
displacement = √(338,400)
displacement ≈ 581.47 m
Therefore, the magnitude of the displacement of the penny is approximately 581.47 meters.