A body at rest explodes into three equal parts, two parts after explosion fly off due north and west respectively with velocity 8m/s then calculate the magnitude and direction of velocity of 3rd pat.

since each part has the same mass, conserving momentum is just conserving velocity:

<0,8> + <-8,0> + <x,y> = 0

or, since the resultant momentum of the two known parts is NW, the 3rd part must go SE.

To find the magnitude and direction of the velocity of the third part, we can use the concept of vector addition. Since the two parts are flying off due north and west, we can represent their velocities as vectors:

Velocity of the first part after explosion = 8 m/s [north] (upwards)
Velocity of the second part after explosion = 8 m/s [west] (leftwards)

Let's consider the third part's velocity as vector v.

To find the resultant velocity (v), we can add the vectors of the first and second parts using vector addition.

Step 1: Draw a graph with a north-south (vertical) and east-west (horizontal) axis.

Step 2: On the graph, draw the vector representing the velocity of the first part. The length of this vector represents the magnitude (8 m/s), and its direction is north.

Step 3: On the graph, draw the vector representing the velocity of the second part. The length of this vector also represents the magnitude (8 m/s), and its direction is west.

Step 4: To find the resultant velocity (v), draw a vector that connects the start point of the first vector (north) with the end point of the second vector (west). This vector represents the magnitude and direction of the velocity of the third part.

Step 5: Measure the length of the resultant vector. This is the magnitude of the velocity of the third part.

Step 6: Measure the angle between the resultant vector and the north direction. This is the direction of the velocity of the third part.

By following these steps, you can determine the magnitude and direction of the velocity of the third part after the explosion.

To calculate the magnitude and direction of the velocity of the third part, we can use vector addition.

Let's assign the following variables:
V1 = velocity of the first part flying due north
V2 = velocity of the second part flying due west
V3 = velocity of the third part (which we need to find)

Given:
V1 = 8 m/s (due north)
V2 = 8 m/s (due west)

Since the velocities of the first and second parts are at right angles to each other, we can combine them using the Pythagorean theorem.

To find V3, we need to find the resultant vector of V1 and V2.

1. Magnitude:
Using the Pythagorean theorem:
V3^2 = V1^2 + V2^2
V3^2 = (8 m/s)^2 + (8 m/s)^2
V3^2 = 64 m^2/s^2 + 64 m^2/s^2
V3^2 = 128 m^2/s^2

Taking the square root of both sides:
V3 = √(128 m^2/s^2)
V3 ≈ 11.31 m/s

So, the magnitude of the velocity of the third part is approximately 11.31 m/s.

2. Direction:
To find the direction of V3, we can use the tangent function.

Using trigonometry:
tan(θ) = opposite/adjacent
tan(θ) = V1/V2

Substituting the values:
tan(θ) = 8 m/s / 8 m/s
tan(θ) = 1

Take the inverse tangent (arctan) of both sides:
θ = arctan(1)

Using a calculator, we find:
θ ≈ 45°

Therefore, the direction of the velocity of the third part is approximately 45° from the west direction.

To express the direction more precisely, we can use compass directions:

The direction of the velocity of the third part is approximately northwest (45° from the west direction).