Calculating Horizontal Distance of Dart Fired by Child on Incline

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SUMMARY

The discussion focuses on calculating the horizontal distance a dart will travel when fired from a dart gun held by a child sliding down a 39.7-degree incline at a speed of 0.869 m/s. The dart gun is fired horizontally from a height of 1.1 m above the ground, and the acceleration due to gravity is 9.8 m/s². Participants explore the correct method to determine the x-component of the child's velocity using trigonometric functions, specifically whether to use sine or cosine. Additionally, the discussion raises the question of how to calculate the muzzle velocity of the dart gun based on the initial conditions.

PREREQUISITES
  • Understanding of basic physics concepts, including projectile motion.
  • Knowledge of trigonometric functions, specifically sine and cosine.
  • Familiarity with the equations of motion under constant acceleration.
  • Ability to perform calculations involving gravitational acceleration (9.8 m/s²).
NEXT STEPS
  • Learn how to calculate projectile motion using initial velocity and height.
  • Study the application of trigonometric functions in resolving vector components.
  • Explore the derivation of muzzle velocity from projectile motion equations.
  • Investigate the effects of incline angles on projectile trajectories.
USEFUL FOR

Students in physics, educators teaching projectile motion, and anyone interested in applying trigonometry to real-world problems involving motion on inclines.

ngoldfarb
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Okay here is the problem:
A dart gun is fired while being held horizontally at a height of 1.55 m above ground level, and at rest relative to the ground. The dart from the gun travels a horizontal distance of 7.77 m. A child holds the same gun in a horizontal position while sliding down a 39.7 degree incline at a constant speed of 0.869 m/s. The acceleration of gravity is 9.8 m/s^2.

What horizontal distance "x" will the dart travel if the child fires the gun forward when it is 1.1m above the ground? Answer in units of m.

I tried finding out how fast the boy would be traveling in the x direction by using: sin 39.7 * 0.869 m/s but once I have that information, I don't know what to do with it. thanks.
 
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ngoldfarb said:
I tried finding out how fast the boy would be traveling in the x direction by using: sin 39.7 * 0.869 m/s but once I have that information, I don't know what to do with it. thanks.
Should you use the sine or cosine to find the x-component of the child's velocity?

From the information provided in the first part, can you determine the muzzle velocity of the dart gun?
 

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