Relative Velocity - is the answer correct?

In summary, the ant's velocity relative to the ground is 68.6mm/s [W18N]. This is calculated by adding the ant's velocity of 20mm/s [W] to the velocity of the stick being dragged at 50mm/s [W25 N], which gives a total velocity of 65.3mm/s [W] and 21.1mm/s [N]. Using the Pythagorean theorem and trigonometry, the resulting velocity is calculated to be 68.6mm/s [W18N].
  • #1
Mezz
2
0

Homework Statement


An ant with a velocity of 20mm/s [W] crawls on a stick that is being dragged [W25 N] at 50mm/s. what is the velocity of the ant relative to the ground?

Homework Equations


Let A = ant, Let S=stick, Let G=ground, Let N and W be positive. Vag=?, Vas=20mm/s [W], Vsg=50mm/s[W25N]

The Attempt at a Solution


Vag=Vas + Vsg

Vas = Vasx + Vasy
= 20mm/s + 0mm/s

Vsgx = Vsg(cos25)
=50mm/s(cos25)
=45.315 mm/s

Vsgy= Vsg(sin25)
=50mm/s(sin25)
=21.130mm/s

Vagx=Vasx +Vsgx
=20mm/s+45.315mm/s
=65.3mm/s

Vagy= Vasy + Vsgy
= 0mm/s +21.130mm/s
=21.1mm/s

V2ag=V2agx +V2agy
Vag= (65.3mm/s)2+(21.1mm/s)2 - This is square root as well
Vag=68.6mm/s

Tan@= O/A
@= Tan-1(21.1mm/s / 65.3mm/s)
@= 17.9
@=18

Therefore the Ant s velocity relative to the ground is 68.6mm/s [W18N]
 
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  • #2
That's what I get as well.
 
  • #3
BiGyElLoWhAt said:
That's what I get as well.
Thank you!
 

Related to Relative Velocity - is the answer correct?

1. What is relative velocity?

Relative velocity is the velocity of an object or observer in relation to another moving object or observer. It takes into account the motion of both objects and their direction of movement.

2. How is relative velocity calculated?

Relative velocity is calculated by subtracting the velocity of the reference frame from the velocity of the moving object or observer. This can be represented mathematically as V rel = V obj - V ref.

3. Can relative velocity be negative?

Yes, relative velocity can be negative if the moving object or observer is going in the opposite direction of the reference frame. This indicates that the objects are moving away from each other.

4. What is the difference between relative velocity and absolute velocity?

Absolute velocity is the velocity of an object or observer relative to a fixed point, while relative velocity takes into account the motion of another object or observer. Absolute velocity does not change, while relative velocity can vary depending on the reference frame.

5. How does relative velocity affect collisions between objects?

Relative velocity plays a crucial role in collisions between objects. The relative velocity between the two objects determines the amount of kinetic energy transferred during the collision, and can also determine the direction of the resulting motion after the collision.

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