Projectile Motion- Deriving equation

AI Thread Summary
To derive the time-of-flight for a projectile launched from height h with initial speed v0 at an angle θ, the formula is t = (v0 * sin(θ) + √((v0 * sin(θ))^2 + 2gh)) / g. For the range of the projectile, the expression is R = v0 * cos(θ) * t, where t is the previously derived time-of-flight. Both equations incorporate gravitational acceleration g and the launch parameters. The discussions focus on the algebraic manipulation of these variables to arrive at the desired expressions. Understanding these derivations is essential for solving projectile motion problems effectively.
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Homework Statement



Part 1- Derive an algebraic expression for the time-of-flight of a projectile launched with initial speed v0 from a height h at an angle θ above horizontal. (Use any variable or symbol stated above along with the following as necessary: g. Do not substitute numerical values; use variables only.)

Part 2- Derive an algebraic expression for the range of a projectile launched with initial speed v0 at an angle θ above horizontal with time-of-flight t. (Use the variable t in your answer. Do not substitute the expression for t found above.)


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