Solve Velocity Equation: -g(horizontal distance)/sin(2theta)

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SUMMARY

The discussion centers around the velocity equation for projectile motion: velocity = sqrt((-g)(horizontal distance)/sin(2theta)). The user questions the validity of the equation, particularly when applied to a scenario involving a ball thrown at an angle of 26 degrees with a horizontal distance of 290 feet and gravitational acceleration of -32 ft/s². The calculated velocity of approximately 108.52 ft/sec raises doubts, especially when compared to personal experience with a different throw angle and distance. The user seeks clarification on the equation's correctness and application.

PREREQUISITES
  • Understanding of basic physics concepts, particularly projectile motion.
  • Familiarity with trigonometric functions, specifically sine and angles.
  • Knowledge of gravitational acceleration, particularly -32 ft/s² in the context of Earth.
  • Ability to manipulate and solve algebraic equations involving square roots.
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  • Research the derivation of the projectile motion equations, focusing on the maximum distance formula.
  • Learn about the significance of the angle of projection in determining the trajectory of a projectile.
  • Explore the implications of gravitational acceleration on projectile motion calculations.
  • Investigate real-world applications of projectile motion equations in sports and engineering.
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Students studying physics, educators teaching projectile motion, and anyone interested in understanding the dynamics of objects in motion under gravity.

LT72884
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So i was googling the mighty google for a general question on velocity and i happened upon this equation with no description of it. Only states it is a velocity equation

velocity=sqrt((-g)(horizontal distance)/sin(2theta))

sorry, symbols is not working on me laptop at the moment

Its been a LONG while since physics for me but i do not recal this equation.

an example was given of:
distance a ball was thrown = 290 feet
g= -32
angle ball was thrown was 26* ( i assume horizontal is 0* but sin 0 = o which can't have in denominator so something seems odd)

they end up with roughly 108.52 ft/sec

this eq seems strange to me. i threw a ball at roughly 8* and it took 1.002 seconds to go 15feet. if i plug that into me equation i get 42 feet/s

that doesn't sound right to me because after 1.002 seconds, the ball landed at 15 feet, so it can't be going 42 feet/sec then.

ANYWAY my MAIN QUESTION IS... WHAT EQUATION IS THIS HAHAHA

thanks
 
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