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Projectile Motion Equations

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Questions and Answers

Match the following quantities with their respective formulas:

Range of a projectile = $R = (v₀²sin(2θ)) / g$ Maximum height of a projectile = $H = (v₀²sin²(θ)) / (2g)$ Initial velocity of the projectile = Not applicable Acceleration due to gravity = Not applicable

Match the following variables with their descriptions:

$v₀$ = Initial velocity of the projectile $θ$ = Angle of projection (measured from the horizontal) $g$ = Acceleration due to gravity $R$ = Range of the projectile

Match the following concepts with their definitions:

Range of a projectile = Horizontal distance traveled from point of projection to point where it hits the ground Maximum height of a projectile = Highest point reached during trajectory Trajectory = Path of the projectile's motion Angle of projection = Angle at which the projectile is projected from the ground

Match the following equations with their corresponding physical quantities:

$R = (v₀²sin(2θ)) / g$ = Range of a projectile $H = (v₀²sin²(θ)) / (2g)$ = Maximum height of a projectile $v₀ =...$ = Not applicable $g = 9.8 m/s²$ = Acceleration due to gravity Signup and view all the answers

Match the following conditions with their corresponding events:

Vertical component of velocity is zero = Maximum height is reached Projectile hits the ground = Range is reached Projectile is projected = Initial velocity is achieved Projectile reaches its maximum height = Vertical component of velocity is not zero Signup and view all the answers

Match the following quantities with their units:

Range of a projectile = meters Maximum height of a projectile = meters Acceleration due to gravity = m/s² Initial velocity of the projectile = m/s Signup and view all the answers

Study Notes

Range of a Projectile

The range of a projectile is the horizontal distance it travels from the point of projection to the point where it hits the ground.
The range of a projectile is given by the equation:

R = (v₀²sin(2θ)) / g

where: + R is the range of the projectile + v₀ is the initial velocity of the projectile + θ is the angle of projection (measured from the horizontal) + g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)

Maximum Height of a Projectile

The maximum height of a projectile is the highest point it reaches during its trajectory.
The maximum height of a projectile is given by the equation:

H = (v₀²sin²(θ)) / (2g)

where: + H is the maximum height of the projectile + v₀ is the initial velocity of the projectile + θ is the angle of projection (measured from the horizontal) + g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)

The maximum height is reached when the vertical component of the velocity is zero, i.e., at the apex of the trajectory.

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Description

Test your knowledge of projectile motion equations, including range and maximum height calculations. Learn how to apply these formulas to real-world problems.