How Does Relative Motion Affect Velocity Calculations?

[afraidofdark]

hello, I have a simple question.
a long vehicle' s velocity is 26 m/s , a person on the vehicle runs at -6 m/s, what is his velocity ? I think it is 20 m/s from an inertial frame
However, imagine this situation, an elevator is at free falling and just before it collide it has 26 m/s and a person in the elevator jump at 6 m/s just before the collision. would impulse effect decrease ?

this question in my book solved like this; boy is 90kg

26 m/s - (-6m/s) = 32 m/s
impulse = final moment - initial moment
= 0*90 - 32*90
= -2880

why did he subtract -6 velocity ? If the boy jump, wouldn't his velocity become 20 m/s from an inertial frame ?

thank you for your helps

 

[LightHero]

.The answer to your question is yes, the person's velocity would be 20 m/s from an inertial frame. The calculation the book provided was used to calculate the impulse of the person jumping, which is defined as the change in momentum (in this case, the change in the velocity multiplied by the mass). Since the initial velocity was -6 m/s and the final velocity was 26 m/s, the change in velocity was 32 m/s. Therefore, the impulse of the person is equal to 32m/s * 90kg = 2880 Ns.

 

[astrokreng]

In this scenario, the person's velocity would not be 20 m/s from an inertial frame. The velocity of the person is relative to the platform, not to the ground. Therefore, the person's velocity would be -6 m/s relative to the platform, and 20 m/s relative to the ground.

In terms of impulse, the negative sign represents the direction of the force. In this case, the force is acting in the opposite direction of the boy's motion, so it is negative. The subtraction of the boy's velocity is to account for the direction of the force and calculate the change in momentum.

In the case of the elevator, the person's velocity would not decrease due to the impulse effect. The impulse effect is based on the change in momentum, which is determined by the force and time of interaction. In a free-falling elevator, there is no external force acting on the person, so their velocity would remain the same. However, if the elevator were to collide with something, the person's velocity would change due to the impulse effect of the collision.