Dynamics trajectory motion help

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SUMMARY

The discussion revolves around calculating the initial speed of a car at ramp A to ensure it covers a horizontal distance of 180 feet while descending at angles of 15° and 30°. The key hint provided indicates that the initial speed can be determined by finding the intersection of the car's parabolic trajectory and a straight line defined by the slope of tan(30°). The equations of motion under constant acceleration, specifically with gravitational acceleration set at 32.2 ft/sec², are crucial for solving this problem.

PREREQUISITES
  • Understanding of projectile motion and parabolic trajectories
  • Familiarity with trigonometric functions, particularly tangent
  • Knowledge of equations of motion under constant acceleration
  • Basic skills in algebra for solving equations
NEXT STEPS
  • Study the equations of motion for projectile trajectories
  • Learn how to apply trigonometric functions in physics problems
  • Research methods for finding intersections of curves and lines
  • Practice similar projectile motion problems involving angles and distances
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Students in physics or engineering courses, particularly those focusing on mechanics and projectile motion, will benefit from this discussion.

UCF_Martin
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Homework Statement


"In a movie scene involving a car chase, a car goes over the top of ramp A and lands a B below. Determine the speed of the car at A if the car is to cover distance d=180ft for \alpha =15° and \beta = 30°. Neglect aerodynamic effects.


Homework Equations


Word.doc is the problem picture.


The Attempt at a Solution


I have calculated the distance the car moves the in X, and falls in the Y. But other than that I am rather lost mathematically.

The hint for the problem states: "The required initial speed can be found from the intersection of the parabolic trajectory and the straight line whose slope in determined by tanβ"

Only problem is I have no idea as to what line tanβ is the slope of.
 

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Hi UCF_Martin,

As the car becomes airborne at point A, two things happen: (i) it continues to travel horizontally with the same horizontal component of speed as it had at point A, and (ii) its vertical motion is controlled by gravity.

You should be able to quote in your sleep a set of equations describing motion under a constant acceleration (g = 32.2 ft/sec).
 
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