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Projectile motion of car hitting the ground

  1. Mar 21, 2013 #1
    1. The problem statement, all variables and given/known data
    (Assume no friction) A car that has a mass of 3970 kg is accelerated from an initial velocity of 0 up a ramp that is 50 meters long (the hypotenuse) and has a height above the ground at the end of the ramp of 10 meters. The velocity of the car at the end of the ramp is 150 km/hr. At the end of the ramp the car flies through the air as a projectile. What is the angle of the ramp in degrees? If the car starts up the ramp at time equal to 0 seconds, how many seconds later does the car hit the ground.



    2. Relevant equations



    3. The attempt at a solution
    I know I have to solve for the initial velocities in the x and y direction but I honestly have no idea where to start in this problem--if anyone could just tell me a starting point--it'd be much appreciated.
     
    Last edited by a moderator: Aug 30, 2015
  2. jcsd
  3. Mar 21, 2013 #2
    The angle of the velocity is the angle of the ramp. Which you should determine from the sides given. Recall how the sine is defined.
     
  4. Mar 21, 2013 #3
    I found the angle to be 11.53 degrees, what can I do from there?
     
  5. Mar 21, 2013 #4
    How can you find x and y velocity ccomponents given the sine of the angle and the magnitude of the velocity?
     
  6. Mar 21, 2013 #5
    I don't know. I was never taught that--he gave us a problem set and gave us 2 days to solve it.
     
  7. Mar 21, 2013 #6
    If you knew the x and components of the initial velocity, would you be able to solve the problem?
     
  8. Mar 21, 2013 #7
    I believe so, yes
     
  9. Mar 21, 2013 #8
    Very well. If some velocity has components Vx and Vy, what is the magnitude of the velocity?
     
  10. Mar 21, 2013 #9
    Wouldn't it be the SQRT(Vx^2+Vy^2) ? Using Pythagorean theorem?
     
  11. Mar 21, 2013 #10
    That is correct. The components-magnitude stuff works like sides in a right triangle. So how can you get the components if you know the magnitude ( = hypotenuse) and the angle?
     
  12. Mar 21, 2013 #11
    Oh, just you trigonometric functions and you get the y direction to be 10, and the x direction to be 49?
     
  13. Mar 21, 2013 #12
    These are the sides of the ramp. You need to find the "sides" of velocity.
     
  14. Mar 21, 2013 #13
    knowing that the magnitude of velocity is 150 km/hour?
     
  15. Mar 21, 2013 #14
    Yes.
     
  16. Mar 21, 2013 #15
    ok i changed the magnitude to m/sec to make it easier so it'd be 41.67 m/sec, that'd mean that the x direction it would equal 40.8 m/sec and the y direction would equal 8.3 m/sec. right?
     
  17. Mar 21, 2013 #16
    Correct.
     
  18. Mar 21, 2013 #17
    Would I now plug everything I have into the projectile motion equations?
     
  19. Mar 22, 2013 #18
    Well, you said that given Vx and Vy you should be able to solve the problem. What is difficulty now?
     
  20. Mar 22, 2013 #19
    I was unsure--I managed to solve it.
     
  21. Mar 22, 2013 #20
    Good job!
     
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