Solve Kinematic Problem: Man Shot from Cannon onto Net

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SUMMARY

The kinematic problem involves a man shot from a cannon with an initial velocity of 10 m/s at a 60-degree angle, starting from a height of 6.5 meters and landing on a net positioned 2.5 meters above the ground. To determine the time of flight, horizontal distance to the net, and final velocity upon landing, one must calculate the initial velocity components using trigonometric functions: Vxi = 10 m/s * cos(60°) and Vyi = 10 m/s * sin(60°). The vertical motion can be analyzed separately to find the time of ascent and descent, while the horizontal motion remains constant, allowing for straightforward calculations of distance and final velocity.

PREREQUISITES
  • Understanding of projectile motion principles
  • Knowledge of trigonometric functions (sine and cosine)
  • Familiarity with equations of motion
  • Basic concepts of energy conservation in physics
NEXT STEPS
  • Calculate the initial horizontal and vertical velocity components using Vxi and Vyi.
  • Apply the equations of motion to determine the time of flight for the projectile.
  • Determine the horizontal distance to the net using the constant horizontal velocity.
  • Analyze the final velocity vector upon landing, including both magnitude and direction.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding projectile motion and kinematic analysis in real-world applications.

Thekhan
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In this particular act, a man is shot out of a cannon with an initial velocity of 10 m/s at an angle of 60 degrees onto a net at some distance away. The cannon is 6.5m above the ground, and the net is 2.5m above the ground.

How long does it take for the man to land on the net?
how far is the net from the cannon?
what is the magnitude and direction of the man's velocity when he lands on the net?

I'm sort of lost on this problem, i know I'm supposed to find the Vxi and Vyi via cos and sin but i am not sure where to go from there, please help.
 
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take the x and y components of velocity, and solve them separately with help of equations of motion.

PS: Show how you work out from next time.
 
Note that the X and Y components can be treated independantly. Just take the vertical component (Y) alone and find out the time it takes to go up and come back (ignore wind resistance). During that time, the horizontal component is constant (ignoring wind resistance). Once you find the time to land, then distance is horizontal velocity multiplied by time. When he lands on the net, the vertical component is the same as the initial vertical component (assuming no wind resistance) and horizontal is same. So this essential means that energy is not destroyed!
 

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