Solving 2D Motion: Find Time & Velocity

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SUMMARY

The discussion focuses on solving a 2D motion problem involving a stone thrown at a 45-degree angle on a downward sloping field with a 5-degree angle. The key equations derived include the range equation \( R = \frac{V_i^2 \sin(2\theta_i)}{g} \) and the calculations leading to an initial velocity \( V_i \) of 21.72 m/s. The time of flight is determined using the relationships between the vertical and horizontal components of motion, with gravitational acceleration set at \( g = 9.8 \, \text{m/s}^2 \). The problem emphasizes the use of symmetry in projectile motion and the independence of motion in different directions.

PREREQUISITES
  • Understanding of 2D projectile motion principles
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of kinematic equations and gravitational acceleration
  • Ability to solve systems of equations
NEXT STEPS
  • Study the derivation of the range equation for projectile motion
  • Learn about the independence of horizontal and vertical motion in physics
  • Explore the application of energy conservation in projectile motion problems
  • Investigate numerical methods for solving motion equations, such as integration techniques
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This discussion is beneficial for physics students, educators, and anyone interested in mastering the concepts of projectile motion and solving related problems in mechanics.

Atilla1982
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2d Motion

I've been stuck with this problem for a while. Appreciate if anyone can point me in the right direction.

A boy stands in a field, he throws a stone with an initial 45 degree angle. The field has a 5 degree angle downwards, so the stone touches down at -5 degree angle and 82 meters away. g=9,8m/s^2

Find the time (t) for the entire throw, and the initial velocity (v0) for the stone.
 
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sin45*v0*t=82*cos50
sin45*v0=g*t1
2*t1+t2=t
sin45*v0*t2+0.5*g*t2^2=82*sin50

4 equations for 4 unknows

we use the symmetry of the motion, and the independence of the motions in different directions
 
sorry, cos50 and sin50 above mean cos5 and sin5
 
and you can also use energy , but i don't think it woulb be much more easier
 
couldn't i do: R=Vi^2*sin2(THETAi)/g

R=the length of the throw

Solving for Vi= 21.72 m/s
 
And then set up an integral for time?
 

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