a dog walks 28 steps north and then walks 55 steps west. if the daog walks back to the starting point in a straight line, how many steps will the dog take? find the magnitude of the net displacement

Use the distance relation:

distance= sqrt( Nsteps^2 + Wsteps^2)

To find the total number of steps the dog takes, we need to consider both the north and west directions.

The north direction has a displacement of 28 steps, and the west direction has a displacement of 55 steps. Since the dog walks back to the starting point in a straight line, we can find the total displacement using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

So, the total displacement is:

displacement^2 = (north displacement)^2 + (west displacement)^2

displacement^2 = 28^2 + 55^2
displacement^2 = 784 + 3025
displacement^2 = 3809

Taking the square root of both sides, we can find the magnitude of the net displacement:

displacement = โˆš3809
displacement โ‰ˆ 61.72 (rounded to the nearest hundredth)

Therefore, the dog will take approximately 61.72 steps, and the magnitude of the net displacement is approximately 61.72.

To find the total number of steps the dog will take and the magnitude of its net displacement, we can use the Pythagorean theorem.

First, let's break down the dog's movements:

- The dog walks 28 steps north.
- The dog then walks 55 steps west.

To find the total number of steps the dog will take, we need to find the hypotenuse of the right triangle formed by the north and west distances.

Using the Pythagorean theorem, we have:
Hypotenuse^2 = North^2 + West^2

Substituting the values we have:
Hypotenuse^2 = 28^2 + 55^2

Simplifying the equation:
Hypotenuse^2 = 784 + 3025
Hypotenuse^2 = 3809

Taking the square root of both sides to solve for Hypotenuse:
Hypotenuse = sqrt(3809)
Hypotenuse โ‰ˆ 61.72 (rounded to two decimal places)

Therefore, the dog will take approximately 61.72 steps to return to the starting point.

To find the magnitude of the net displacement, we can simply take the hypotenuse value:
Magnitude of net displacement = 61.72 steps