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A projectile is fired horizontally from a gun that is 45.0 m above flat ground. What is the acceleration of the projectile in the vertical direction?
A projectile is fired horizontally from a gun that is 45.0 m above flat ground. What is the acceleration of the projectile in the vertical direction?
g = 9.8 m/s^2
Jason Renie sets a world-record motorcycle jump of 77.0 m. What is the angle of elevation of the take-off ramp?
Jason Renie sets a world-record motorcycle jump of 77.0 m. What is the angle of elevation of the take-off ramp?
12.0º
A soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45°. What is the time of flight of the ball?
A soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45°. What is the time of flight of the ball?
2.81 s
You throw a ball toward a wall at speed 25.0 m/s and at angle 40.0° above the horizontal. What is the horizontal component of its velocity as it hits the wall?
You throw a ball toward a wall at speed 25.0 m/s and at angle 40.0° above the horizontal. What is the horizontal component of its velocity as it hits the wall?
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A projectile is fired horizontally from a gun that is 45.0 m above flat ground. How long does it take for the projectile to strike the ground?
A projectile is fired horizontally from a gun that is 45.0 m above flat ground. How long does it take for the projectile to strike the ground?
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A soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45°. What is the average speed required for the player to meet the ball just before it hits the ground?
A soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45°. What is the average speed required for the player to meet the ball just before it hits the ground?
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What is the shape of the path of a projectile, and how can it be proven?
What is the shape of the path of a projectile, and how can it be proven?
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How do the horizontal and vertical motions of a projectile affect each other?
How do the horizontal and vertical motions of a projectile affect each other?
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What is the equation for the horizontal range of a projectile?
What is the equation for the horizontal range of a projectile?
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What is the characteristic of the vertical motion of a projectile?
What is the characteristic of the vertical motion of a projectile?
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What is the relationship between the horizontal and vertical components of velocity in a projectile?
What is the relationship between the horizontal and vertical components of velocity in a projectile?
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How does the initial velocity of a projectile affect its trajectory?
How does the initial velocity of a projectile affect its trajectory?
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What is the significance of the stroboscopic photograph of two golf balls?
What is the significance of the stroboscopic photograph of two golf balls?
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What is the condition for which the equation for horizontal range does not apply?
What is the condition for which the equation for horizontal range does not apply?
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Study Notes
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.
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Description
Solve problems related to projectile motion, including time in the air, horizontal distance, and velocity components.
