Question

A man travels 4 m West, then 1 m North. Calculate the magnitude of his displacement

Answer 1

Answer:
`√(17)`m

Step-by-step explanation:

lets draw your question first. lets see

4m west = AB

1m north = BC

AB⊥BC (west is 90° from north)

it will be a right-angled triangle if you drew it correctly

we can find the magnitude if we find AC for this we can use the Pythagorean theorem

a² + b² = c²

AB² + BC² = AC²

4² + 1² = AC²

AC² = 17

AC =
`√(17)`

Answer 2

The magnitude of the man's displacement after traveling 4 m West and then 1 m North is 4.12 meters, calculated using the Pythagorean theorem.

Step-by-step explanation:

The question is asking to calculate the magnitude of the man's displacement after he travels in two different directions. Displacement is a vector quantity that represents the change in position of an object and is independent of the path taken. Here, the man travels first 4 meters West and then 1 meter North. The displacement in this case can be calculated using the Pythagorean theorem since the two directions are perpendicular to each other (forming a right-angled triangle).

To find the magnitude of his displacement, we calculate the hypotenuse of the triangle formed by his two movements:

• Displacement to the West (along the x-axis): 4 m
• Displacement to the North (along the y-axis): 1 m

The magnitude of the displacement (R) is given by the equation:

R = √(x² + y²)

Plugging in the values:

R = √((4 m)² + (1 m)²) = √(16 + 1) = √(17) = 4.12 m (to two decimal places)

Therefore, the magnitude of the man's displacement is approximately 4.12 meters.