Question

Topic: Graphical representation of vectors

Question: Two Trucks are moving at a particular speed and direction. If the first truck is moving with a velocity of 2m/s towards the east and the other truck is moving with a velocity of 4m/s toward the South East. Find the resultant velocity if both the truck collide.
In which direction will they go?

Represent by graph method only. I don't need a formula.

Answer 1

Given :

• Velocity and direction of truck A = 2m/s toward east .

$\implies \tt{ \overrightarrow{a} = 2mps \: to \: east}$

• Velocity and direction of truck B = 4m/s To West

$\tt{ \implies \overrightarrow{b} = 4mps \: to \: south \: east}$

To Find :

• The resultant vector after the collision

$\implies \tt{ \overrightarrow{r} =\overrightarrow{a} + \overrightarrow{b}}$

• Direction of the resultant vector.

Process:

To represent graphically, first we will arrange the vectors as two sides of triangles.

According to the triangle law: If the two vectors are arranged as two sides of triangle in the same order , then the third side is the resultant in opposite order.

So, we will solve the question with this law.

To find direction, the angle between vector A and R will be the direction.

Note : Please see the figure for more clearer information.

Solution :

First, We will draw these two vectors on a graph sheet.

Here, We will take

• 1 mps = 1 cm
• 2 mps = 2cm
• 4 mps = 4cm

See the figure 1 for the position of vectors A and Vector B

_______________________

Now, as we know, parallel shifting is allowed in vectors,

So, we will shift the vector B such that its head is in the tail of vector A. .

These two vectors are like two sides of triangle

See the figure 2 .

_______________________

As said in triangle law, the third side of triangle is the resultant Vector with opposite order.

So, we will mark the third side of triangle.

Now, with scale find the value of Resultant vector R.

The obtained is the magnitude of vector R.

We get from the figure that :

magnitude of vector R = 5.58 m/s

See the figure 3.

_______________________

Now, To Find the direction, we have to find the Angle between vector A and vector R.

The angle is 30.35° .

Hence, we get that Direction of vector R as :

Vector R is 30.35 ° South from east .

_______________________

Hence, We can say that the resultant Velocity ofter collision is

5.58m/s toward 30.35° South of East.

Answer 2

Answer:

Explanation:Topic: Graphical representation of vectors

Question: Two Trucks are moving at a particular speed and direction. If the first truck is moving with a velocity of 2m/s towards the east and the other truck is moving with a velocity of 4m/s toward the South East. Find the resultant velocity if both the truck collide.

In which direction will they go?

Represent by graph method only. I don't need a formula