Projectile Motion on a Inclined Plane Problem

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SUMMARY

The discussion focuses on solving a projectile motion problem involving an inclined plane, where a bag must be thrown to a friend running up a hill. The key variables include the friend's speed (v_f), the bag's maximum throw speed (v_b), and the hill's angle (\theta). The solution requires determining the optimal angle (\alpha) for throwing the bag, assuming small angles and using trigonometric approximations. Participants emphasize the importance of showing work to facilitate guidance and problem-solving.

PREREQUISITES
  • Understanding of projectile motion principles
  • Basic knowledge of trigonometric functions and approximations
  • Familiarity with inclined plane dynamics
  • Ability to manipulate equations involving angles and velocities
NEXT STEPS
  • Study the equations of motion for projectile motion on an inclined plane
  • Learn about the effects of angle and speed on projectile trajectories
  • Explore trigonometric approximations for small angles
  • Practice similar problems involving projectile motion and inclined planes
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators seeking to enhance their teaching methods in these topics.

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Hi everyone ! My name is Sean. I'm a new member of this forum.
I couldn't do any attempts for this problem. Actually, i did many attemps but they went wrong.

Homework Statement



How can i solve this problem ?
Your friend is late for school and is running with a speed of [itex]v_f[/itex] up a hill which makes an angle of [itex]\theta[/itex] with the horizontal. Just as he run for t seconds he realizes that he has forgotten his schoolbag at the foot o the hill where you are standing. He cannot come back and he must keep running. So you have to throw the bag to him with the largest possible speed you can achieve, which is [itex]v_b[/itex]. If he is still running up the hill what is the angle, [itex]\alpha[/itex] (measured with respect to the inclined plane) with which you should throw the bag to him if the bag is to reach him ?
(Hint : Assume that [itex]\alpha[/itex] is small and use the necessary approximations to the trigonometric functions.)

Thank you.
Sean.
 
Last edited:
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Show us some of your work.

Let's see some equations that you came up with, then we can tell you if you're headed in the right direction.
 

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