Relative Impact Speed

In summary, a curious Physics student is faced with a dilemma of minimizing his relative impact speed while falling from a tower towards an elevator. After considering the one dimensional equations and realizing that going down or up will result in an equal and opposite relative impact speed, the student concludes that the best course of action is to do nothing and let the elevator remain stationary. This will result in the same relative impact speed as if he had hit the down or up button.
  • #1
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Homework Statement



A curious Physics student is inspecting A tower. He slips from a platform near the top and begins to fall straight down. Directly beneath him is an empty elevator at rest part way up the tower wall, and there is a set of control buttons on the platform from which he is slipping. If he does nothing, he will strike the stationary elevator. If he hits the down button, the elevator instantly starts down at a constant speed and he will catch it at a lower point, but before it hits the ground. If he hits the up button, the elevator instantly starts up at the same constant speed and he will meet it at a higher point. Natuerally he wishes to minimize his relative impact speed. What should the Physics student do?


Homework Equations



One dimensional equations


The Attempt at a Solution




Xop = 0.0 m
a = +9.8 m/s
Vop = 0.0 m/s
tp = te
_ _ _ _ _ _

Vo = Ve
Xoe = +h
ae = 0.0 m/s
Ve = ve
te = tp

_ _ _ _ _ _

Xe = Xp

I know that the best method is to keep the elevator stationary but I'm finding it difficult to prove why. I know that going down and up have an equal and opposite relative impact speed.
 
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  • #2
I think that the Physics student should not hit any buttons since the relative impact speed will be the same as if he had done nothing.
 
  • #3
However, if the elevator is stationary, the student will not experience any relative impact speed at all. This is because the elevator and the student will have the same velocity and direction when they meet. Therefore, the impact speed will be zero.

To further support this, we can use the equation for relative velocity:

Vrel = Vp - Ve

If the elevator is stationary (Ve = 0), then the relative velocity is simply equal to the student's velocity (Vrel = Vp). This means that the student and the elevator will have the same velocity when they meet, resulting in a zero relative impact speed.

Additionally, if the student chooses to hit the down button, the elevator will start moving down at a constant speed, which means that the relative velocity will be constantly increasing until the elevator meets the student. This will result in a higher relative impact speed than if the elevator was stationary.

Similarly, if the student hits the up button, the elevator will start moving up at a constant speed, resulting in a decreasing relative velocity. However, the relative impact speed will still be higher than if the elevator was stationary.

In conclusion, the best option for the student is to do nothing and let the elevator remain stationary. This will minimize the relative impact speed and ensure the student's safety.
 

1. What is relative impact speed?

Relative impact speed refers to the velocity at which two objects collide or come into contact with each other. It takes into account the speeds of both objects, as well as their direction of movement.

2. How is relative impact speed calculated?

To calculate relative impact speed, you first need to determine the velocity of each object. Then, you subtract the velocity of one object from the other, taking into account their direction of movement. The resulting number is the relative impact speed.

3. Why is relative impact speed important in scientific research?

Relative impact speed is important in scientific research because it helps us understand the effects of collisions and impacts on objects. This can be useful in fields such as engineering, physics, and geology.

4. Can relative impact speed be negative?

Yes, relative impact speed can be negative. This occurs when the two objects are moving in opposite directions and collide. In this case, one object will have a positive velocity and the other will have a negative velocity, resulting in a negative relative impact speed.

5. How can relative impact speed be reduced?

Relative impact speed can be reduced by decreasing the velocity of one or both objects, or by changing the direction of their movement. This can be achieved through various methods such as braking, changing the angle of approach, or using a cushioning material to absorb some of the impact.

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