MHB Velocity & Horizontal Distance of Person on Water Slide

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To determine the velocity and horizontal distance of a person flying off a water slide ramp, the conservation of energy is the most suitable approach. By applying the equation T1 + V1 + U1 = T2 + V2, all relevant variables must be identified and substituted to solve for velocity. After calculating the velocity at the ramp's exit, projectile motion equations can be used to find the horizontal distance traveled. The initial velocity and angle of the ramp will be crucial for this calculation. This method effectively combines energy conservation with kinematic principles to solve the problem.
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a person slides down a water slide that is 61 m long and has a slope angle of 24 degrees and the end is a ramp with a height of 3.66 m with an angle of 30 degrees to the horizontal determine the magnitude and direction of the velocity of the person when they just fly away from the ramp and the horizontal distance that they fly.

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There are a number of equations that I like to say "have physics in them", as opposed to being merely descriptive. Your equations with physics, in a typical order of presentation, are the following:
  1. Newton's Second Law
  2. Conservation of Energy
  3. Work-Energy Theorem
  4. Conservation of Linear Momentum
  5. Conservation of Angular Momentum

Which of these approaches do you think would be appropriate for this problem?
 
I believe the most appropriate approach would be the conservation of energy ie,

T1+V1+U1-2=T2+V2

Then just find all of the relevant pieces of information from the question and subbing them into the equation and solving for the magnitude and direction of the velocity and well as the max flying distance
 
I would agree that CoE would be the right approach for the first part of this problem (finding the velocity). Once you do that, however, how would you continue?
 
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