a particle is subjected to two displacement as follows: 30m to the northeast and 40m to northwest. what must be third displacement if the particle is to end up at the starting point
a particle is subjected to two displacement as follows: 30m to the northeast and 40m to northwest. what must be third displacement if the particle is to end up at the starting point
notice the right triangle in the vector diagram. 3,4,5 triangle...so 50m is the displacement magnitude
Now for the angle.
sketch it.
I see at the bottom angle, the angle
arccos 30/50-PI/4, E of S. or 8.1 deg E of S
check that.
To end up at the starting point, the particle needs to have a net displacement of zero.
The displacement to the northeast can be represented as a vector with a magnitude of 30m in the positive x-axis direction.
The displacement to the northwest can be represented as a vector with a magnitude of 40m in the negative x-axis direction.
To cancel out these displacements, the third displacement needs to have the same magnitude as the first two displacements but in the opposite direction.
Therefore, the third displacement should be a vector with a magnitude of 30m in the negative x-axis direction.
To find the third displacement required for the particle to end up at the starting point, we need to determine the net displacement resulting from the two given displacements.
First, let's represent the two given displacements on a coordinate system:
- The 30m displacement to the northeast can be represented as (30, 0) since it is along the positive x-axis.
- The 40m displacement to the northwest can be represented as (-40, 0) since it is along the negative x-axis.
Next, let's calculate the net displacement. To do this, we can simply add the two displacements together:
Net Displacement = (30, 0) + (-40, 0)
When we add these values coordinate-wise, we get:
Net Displacement = (30 + (-40), 0 + 0)
= (-10, 0)
The net displacement is (-10, 0), which means the particle has moved 10m to the left (west) without any displacement along the y-axis.
To end up at the starting point, the particle needs to have a displacement equal to the reverse of this net displacement. In other words, it needs to move 10m to the right (east) without any displacement along the y-axis.
Therefore, the third displacement required for the particle to end up at the starting point would be 10m to the east (right).