# cross over to another object that has same height with our last position, is that really possible?

I have got confused with this.

Well..In that picture, lets say the height is 8m, and the car moves and going to cross over to another object that has the same height with its last position..my question is ? is that possible or not ? what makes it's real ? the speed of car ? or the distance between the objects ?

• it is going to crash into the left wall for sure .With a incline at the edge of right position it may cross with enough speed . Try to provide your own attempt at solution in this site or its gonna be removed. Dec 15, 2014 at 16:51
• Why do you think the car will do a jumping? Dec 15, 2014 at 16:56
• i mean...cross over, sorry Dec 15, 2014 at 16:57
• Where does the picture come from? Dec 15, 2014 at 16:57
• i made it.. i did something at home.. my little brother were playing toys, he did like that... the toy crossed over it...because of that i asked question like this.. Dec 15, 2014 at 17:02

If the car starts out going in a straight line, it will drop a little bit in the time it takes to cross the gap. If the drop is larger than the height of the chassis above the ground, the car will crash into the opposite wall. When the drop is less than that (small gap, high speed) and the wheels are able to absorb the shock, it is possible that the car will survive the "jump". Note - if the suspension extends the wheel while the car is in the air, and the axle ends up below the edge of the rim, the car will also crash.

This would be OK:

But this would not be OK:

And neither would this:

For a gap distance $D$ and car's (assumed constant) velocity $v$, the time to cross the gap is $t=D/v$. If you want to be very particular, then the car not only drops - it also rotates in the air (there is a short time when the front wheels are not supported but the rear wheels are, and that will cause some forward rotation. I will omit that from the calculation but it will make the jump even more dangerous).

In a time $t$, the car drops a distance $h=\frac12 g t^2$. So if we determine a "safe drop height" $h_s$ (let's say 10 cm for the center of gravity, recognizing that the wheels will end up lower than that) we can write

$$h_s = \frac12 g \left(\frac{D}{v}\right)^2\\ v = \sqrt{\frac{gD^2}{2 h_s}}$$

Putting in $g=10 m/s^2, D = 6 m, h_s = 0.1 m$ we find a required speed of just over 42 m/s or 150 km/hr. It would be a braver guy than me to drive a car that fast over a "flat" jump... especially because of the consideration of rotation and wheel extension, both of which are likely to make the outcome "non repeatable" (well, not by the same driver).

However, there is a very interesting technology that was developed by Bose a few years ago - the active suspension. It actually allows a car to "really jump". See for example this image (from http://media.caranddriver.com/images/04q4/267422/a-surprising-new-active-suspension-photo-98872-s-429x262.jpg):

Or even several amazing videos, such as https://www.youtube.com/watch?v=eSi6J-QK1lw

• If the distance your car is jumping in the first scenario is approx. 6m and you allow for a free fall of 0.1m (which is probably the most you can do before a straight edge would shred the tires), then the fall time of the front end of the car is approx. 0.14s at a minimum speed of 150km/h... ouch... I don't think that has nearly enough margin to be called a "safe" stunt! Dec 15, 2014 at 17:12
• @CuriousOne - I never suggested you should try this at home... I was just trying to show some of the considerations that go into this. Thanks for adding the math. I will update answer with equations for completeness. Dec 15, 2014 at 17:15
• Thanks for suggesting (a fraction of) the tire size as a useful height difference. I didn't think about that. It is an interesting problem, for sure, and one that people are engaged in solving all the time... and not just for the purpose of entertainment, I suppose. I am sure that there are serious civil engineering concerns of this kind in the design of roads and highways... with the idea of keeping people safe, of course, in case of accidents. Dec 15, 2014 at 17:18
• @CuriousOne - the dynamics of wheels on roads, over bumps, etc is quite interesting. I once wrote an answer related to that: physics.stackexchange.com/a/136109/26969 - it has the same picture of the Bose car in it... Dec 15, 2014 at 17:25