Physics Projectile Motion

Projectile Motion

• A projectile is fired horizontally from a gun 45.0 m above flat ground with a speed of 250 m/s.
• The time the projectile remains in the air can be calculated.
• The horizontal distance from the firing point where it strikes the ground can be determined.
• The magnitude of the vertical component of its velocity as it strikes the ground can be calculated.

Motorcycle Jump

• The current world-record motorcycle jump is 77.0 m, set by Jason Renie.
• The take-off speed of the motorcycle can be calculated assuming a take-off angle of 12.0º to the horizontal and neglecting air drag.

Soccer Ball Kick

• A soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45°.
• The time of flight of the ball can be calculated using the formula: t = ... (formula not provided).
• The player must take a certain time (2.81 s) to meet the ball.
• The player's average speed required to meet the ball just before it hits the ground can be calculated.

Ball Thrown Toward a Wall

• A ball is thrown toward a wall at a speed of 25.0 m/s and at an angle of 40.0° above the horizontal.
• The distance from the release point to the wall is 22.0 m.
• The height above the release point where the ball hits the wall can be calculated.
• The horizontal and vertical components of the ball's velocity as it hits the wall can be calculated.
• Whether the ball has passed the highest point on its trajectory when it hits the wall can be determined.

Projectile Motion

• A projectile is an object that is thrown or launched near the surface of the Earth and follows a curved path under the influence of gravity.
• Examples of projectiles include a batted baseball, a thrown football, a package dropped from an airplane, and a bullet shot from a rifle.

Characteristics of Projectile Motion

• The horizontal and vertical motions of a projectile are independent of each other.
• The horizontal motion of a projectile is constant, while the vertical motion is accelerating due to gravity.

Calculating the Path of a Projectile

• The path of a projectile is a parabola.
• The equation of the path of a projectile is derived from the horizontal and vertical velocity equations.

Equations of Projectile Motion

• Horizontal velocity: v_x = v0x
• Vertical velocity: v_y = v0y - gt
• Equation of the path of a projectile: y = x tan(θ) - (gx^2) / (2v0^2 cos^2(θ))

Horizontal Range and Maximum Horizontal Range

• The horizontal range of a projectile is the maximum horizontal distance it can travel.
• The equation for the horizontal range is R = (v0^2 sin(2θ)) / g
• Caution: This equation does not give the horizontal distance traveled by a projectile when the final height is not the launch height.

Key Concept

• The vertical motion of a projectile does not affect its horizontal motion, and vice versa.