How far will the car go?

Honestly, I was going to add this to my previous post about the jumping car but I didn't because I wanted to finish. So, here it is and more. Actually, I will just make a projectile motion spreadsheet. That way, anytime you want to do a projectile motion problem, you can come here. Maybe this is a bad idea, but I am going to do it anyway.

To start with, I will just say that for projectile motion the horizontal and vertical motions are independent (except for the time it takes). If you want a refresher on projectile motion, here you go. Oh, a couple of assumptions:

  • Object starts at x = 0 m and y = h m.
  • The object is shot at an angle theta above the horizontal with an initial velocity v0
  • There is a constant vertical acceleration g
  • The object leaves the starting point at time t
  • The final vertical position will be on the ground (at y= 0 m)

The x-motion will then be:

i-9bd6d0fd3602a64bf80d69d91ba8bea7-2010-06-04_la_te_xi_t_1_5.jpg

The y-motion will be:

i-e5a222a56bf75a55a8cef262bbfdd2e9-2010-06-04_la_te_xi_t_1_6.jpg

If I want to find out how far this thing will go, I can use the y-motion to solve for the time (I will need the quadratic equation). Then I can take this time and plug it into the x-motion equation to find out how far it goes. Here are the calculations in a spreadsheet.

If I put in an initial velocity of 15 m/s at an angle of 24 degrees with an initial height of 1.5 meters, the car would go about 20 meters (65 feet).

Yeeeee HAWWWWWW. Next, on The Dukes!

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i am glad you calculated this. i wondered how far it flew too.

Police report (page 4) indicates 123 feet of skid marks *before* the toll booth so she was initially going faster than the 53 mph you calculated yesterday.

In the picture

http://blogs.dallasobserver.com/unfairpark/moredfwcrashphotos.jpg

you can see the car in the background of the top-left picture and the skid marks in the off-diagonal pictures shows the car approached at an angle.

65 feet seems reasonable, if not a little high since the car has to skid/grind to a stop upon landing.

Off-topic question.
As anyone who lives by a beach knows, wind surfers / kite boarders can surf up the beach and then turn around and surf back down the beach.

1) How is this possible?
2) Are there certain wind directions where it is impossible? (I suspect it is not possible if the wind is parallel along the beach.)
3) Is it absolutely necessary to have a keel on the âboardâ? Otherwise, how do they manage not to be blown on-shore (or out to sea)? Where is the force to stop acceleration on/off-shore coming from?

EXAMPLE: see http://www.youtube.com/watch?v=9l4O3D27ubk (Fun in the wind at the beach, ocracokewaves)
I notice in this video that in one direction you are looking at the interior of the âsailâ and in the other direction you are looking at the exterior. Although at the beach we noticed that sometimes this didnât apply which we guessed means the wind direction was variable.

Thanks.