Determining the minimum velocity when given height and length

In summary, the conversation discusses a problem where a person is trying to jump over a distance using a horizontal plane and gravity. The formula t = √2h/g is used to calculate the time it takes to land, and the formula v = s/t is used to find the velocity, resulting in a velocity of 19.35 m/s. The question arises if this approach is correct and if the initial velocity should be considered.
  • #1
arhzz
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Homework Statement
A stunt driver wants to jump with his car over several cars parked next to each other (a = 12m). He starts from a horizontal plane which is b = 1,9m above the cars.At what minimum speed does he have to jump off, to make the jump
Relevant Equations
t = √2h/g
Now I've tried looking at the problem like this. Considering that a is the length off the vehicles that he is trying to jump over I would consider that to be s. The plane from which he starts (b) should be the h.

So considering that he is jumping from a horizontal plane, gravity should also play a factor so we put in the g constant.After doing this what I though would be a good idea is to figure out when he would land, meaning how long would he fly.For that I used this formula

t = √2h/g

That should be t = 0,62s

Now what I did was try to find the velocity using this formula

v = s/t

I've gotten the result of 19,35 m/s.

Now the part that is bugging me is am I looking at the problem the correct way? I've given it some tought and I'm not so sure that the velocity I am getting is the right one, should I be looking for Vo? Also the fact that horizontal plane is explicity said also brings a few questions. We haven't really covered that in our class but it is in the script. Should I be looking the problem that way?

Thank you for your help.
 
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  • #2
Your method and result are fine. The horizontal component of velocity does not change.
 
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  • #3
haruspex said:
Your method and result are fine. The horizontal component of velocity does not change.
Thank you for your answer!
 

FAQ: Determining the minimum velocity when given height and length

1. How do you determine the minimum velocity when given height and length?

The minimum velocity can be determined by using the formula v = √(2gh), where v is the velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the object.

2. What is the significance of finding the minimum velocity?

Finding the minimum velocity is important because it allows us to understand the minimum amount of energy needed for an object to reach a certain height and distance. It also helps in predicting the trajectory of the object.

3. Can the minimum velocity be calculated for any object?

Yes, the minimum velocity can be calculated for any object as long as the height and length are known. However, this formula assumes that there is no air resistance or other external forces acting on the object.

4. How does the height and length affect the minimum velocity?

The height and length have a direct relationship with the minimum velocity. As the height and length increase, the minimum velocity required also increases. This is because the object needs more energy to overcome the gravitational force and travel a longer distance.

5. Are there any real-world applications of determining the minimum velocity?

Yes, determining the minimum velocity is crucial in many real-world applications such as designing roller coasters, launching satellites, and calculating the minimum takeoff speed for airplanes. It is also used in sports such as long jump and pole vault to determine the minimum velocity needed to clear a certain height.

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