21st October 2019

calculus7

11

What angle maximizes the range of a projectile?

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To maximize the range with respect to the firing angle θ we differentiate R with respect to θ and set this equal to 0. g 2 ∙ cos 2θ ( ) ∙ 0 therefore 2θ π 2 from which we obtain θ π 4 or 45 degrees. Suppose now we fire the projectile up a ramp which makes an angle α with respect to the horizontal. 1.

Likewise, people ask, what is the angle for maximum range?

Maximum Range. Imagine a cannonball launched from a cannon at three different launch angles - 30-degrees, 45-degrees, and 60-degrees. The launch speed is held constant; only the angle is changed. Imagine as well that the cannonballs do not encounter a significant amount of air resistance.

How does the angle affect the distance?

Vertical Distance. The vertical distance, or height, of the ball when thrown or kicked increases when you launch it at a greater angle. As the ball travels upward on its parabolic flight path, the vertical distance it travels decreases because the vertical velocity is decreasing against the push of gravity.

What is the best angle to throw a ball?

Most people know that a ball without air resistance (traditional projectile motion) goes the farthest if you throw it at a 45 degree angle.

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How does the angle affect the distance?

Vertical Distance. The vertical distance, or height, of the ball when thrown or kicked increases when you launch it at a greater angle. As the ball travels upward on its parabolic flight path, the vertical distance it travels decreases because the vertical velocity is decreasing against the push of gravity.

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What is the vertical velocity at the maximum height of a projectile?

As the projectile continues to move upwards, the vertical velocity decreases at a rate of 9.81 meters per second squared (acceleration due to gravity). When the projectile reaches the top of the trajectory (its maximum height), the vertical component of velocity is zero.

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What does the range of a projectile mean?

Now we modify our theory for the horizontal range and derive the range of a projectile on a slope. Assuming a projectile is launched from the ground level, the range is defined as the distance between the launch point and the point where the projectile hits the ground.

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What is the maximum height?

A projectile is an object that is given an initial velocity, and is acted on by gravity. The maximum height of the object is the highest vertical position along its trajectory. The maximum height of the projectile depends on the initial velocity v₀, the launch angle θ, and the acceleration due to gravity.

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What is horizontal range in physics?

A projectile is an object that is given an initial velocity, and is acted on by gravity. The horizontal range of a projectile is the distance along the horizontal plane it would travel, before reaching the same vertical position as it started from.

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What is horizontal displacement?

It was also discussed earlier, that the force of gravity does not influence the horizontal motion of a projectile. The horizontal displacement of a projectile is only influenced by the speed at which it moves horizontally (v_ix) and the amount of time (t) that it has been moving horizontally.

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What is the angle for maximum range?

Maximum Range. Imagine a cannonball launched from a cannon at three different launch angles - 30-degrees, 45-degrees, and 60-degrees. The launch speed is held constant; only the angle is changed. Imagine as well that the cannonballs do not encounter a significant amount of air resistance.

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How does air resistance affect the motion of a projectile?

Objects moving through air are slowed down due to air resistance, sometimes called drag. When air resistance is taken into account the trajectory of a projectile is changed. The resistance is often taken as being proportional to either the velocity of the object or the square of the velocity of the object.

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What angle is best for distance?

The sine function reaches its largest output value, 1, with an input angle of 90 degrees, so we can see that for the longest-range punts 2θ = 90 degrees and, therefore, θ = 45 degrees. A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees.

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What is not true about projectile motion?

b. TRUE - The only force on a projectile is gravity; air resistance must not be present or must not have an influence upon the motion of the projectile. c. FALSE - Projectiles can be moving either upward or downward or at an angle to the vertical.

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What do you mean by time of flight?

A time-of-flight camera (ToF camera) is a range imaging camera system that resolves distance based on the known speed of light, measuring the time-of-flight of a light signal between the camera and the subject for each point of the image.

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What is Time of Flight in projectile motion?

The amount of time it spends in the air is called the time of flight. If the ground from which the projectile is launched is level, the time of flight only depends on the initial velocity v₀, the launch angle θ, and the acceleration due to gravity. The unit for the time of flight is seconds (s).

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How does mass affect a projectile?

Mass does not affect the speed of falling objects, assuming there is only gravity acting on it. Both bullets will strike the ground at the same time. The horizontal force applied does not affect the downward motion of the bullets -- only gravity and friction (air resistance), which is the same for both bullets.

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What is launch angle in physics?

The initial launch angle (0-90 degrees) of an object in projectile motion dictates the range, height, and time of flight of that object.

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What is the definition of range in physics?

In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a predictable range. d is the total horizontal distance travelled by the projectile.

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What is a projectile motion in physics?

And an object which is thrown upward at an angle to the horizontal is also a projectile (provided that the influence of air resistance is negligible). A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.

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How does velocity affect the motion of a projectile?

A projectile will travel the farthest when launched at a 45˚ angle. Initial Speed (m/s) Does not affect the vertical motion. Does affect the horizontal motion. The higher the initial speed, the farther the projectile travels.

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Is a thrown ball a projectile?

An object that is thrown, kicked or otherwise launched through the air is called a projectile. The study of how projectiles move through the air is called projectile motion. In this experiment you will throw a ball as hard as you can while changing the ball's initial angle relative to the ground.

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What does it mean to be in free fall?

Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: Free-falling objects do not encounter air resistance.

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