I need an experiment or a hypothesis to show this. or a method :) thank you.
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How does the angle at which an object is projected affects the horizontal range?
The website below shows the relation ship between the angle and the horizontal range.
http://en.wikipedia.org/wiki/Trajectory
The equation for range is shown below:
Range = (Velocity^2 / g) * sin 2θ
Let velocity = 10 m/s, and vary the angle.
At 10˚, R = 100/9.8 * sin 20˚ = 3.49
At 30˚, R = 100/9.8 * sin 60˚ = 8.84
At 45˚, R = 100/9.8 * sin 90˚ = 10.2
At 60˚, R = 100/9.8 * sin 120˚ = 8.84
At 80˚, R = 100/9.8 * sin 160˚ = 3.49
Notice that the Range increases to the maximum amount at 45˚
The graph of the range vs angle is the top half of a sin curve.
You can see this at the website below.
http://www.delsearegional.us/alumni/year…
Use a compressed spring to propel a small object up an inclined plane and into the air. Vary the angle of the inclined plane and measure the horizontal distance the object moves after leaving the inclined plane.
The website below shows the relation ship between the angle and the horizontal range.
http://en.wikipedia.org/wiki/Trajectory
The equation for range is shown below:
Range = (Velocity^2 / g) * sin 2θ
Let velocity = 10 m/s, and vary the angle.
At 10˚, R = 100/9.8 * sin 20˚ = 3.49
At 30˚, R = 100/9.8 * sin 60˚ = 8.84
At 45˚, R = 100/9.8 * sin 90˚ = 10.2
At 60˚, R = 100/9.8 * sin 120˚ = 8.84
At 80˚, R = 100/9.8 * sin 160˚ = 3.49
Notice that the Range increases to the maximum amount at 45˚
The graph of the range vs angle is the top half of a sin curve.
You can see this at the website below.
http://www.delsearegional.us/alumni/year…
Use a compressed spring to propel a small object up an inclined plane and into the air. Vary the angle of the inclined plane and measure the horizontal distance the object moves after leaving the inclined plane.
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Range R =Vi²*sin(2Θ)/g
So,
The range varies with the sine of twice the angle of elevation of the initial velocity.
So,
The range varies with the sine of twice the angle of elevation of the initial velocity.
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Neglecting friction from air, any object will continue to move at the same horizontal velocity until it comes to rest after impacting the ground. If one projects the object in a horizontal plane, it will begin to fall immediately due to gravity and will impact the ground sooner than if it had an upward arch. The angle of that upward arch has the effect of keeping the object airborne for a longer time, allowing the object to move horizontally for a longer time (and cover a greater distance) before impact.
Gravitational force (a constant) begins to act on the object immediately after it is released, but that force must first reverse the upward movement before the object can start to fall.
For example, if an object slides off a 16' high table at 32 ft/s, it will take 1 second to strike the ground and it will have traveled 32 ft horizontally in that time. If it is launched upward at 30 degrees, after 1 second it will have reached the top of its "arch" and will then start back down. From there it will take about another 1.5 seconds to reach the ground, but since horizontal motion continues it will have stayed airborne for 2.5 seconds and in that time it will have covered about 70 feet!
The maximum distance is when the angle is 45 degrees.
Gravitational force (a constant) begins to act on the object immediately after it is released, but that force must first reverse the upward movement before the object can start to fall.
For example, if an object slides off a 16' high table at 32 ft/s, it will take 1 second to strike the ground and it will have traveled 32 ft horizontally in that time. If it is launched upward at 30 degrees, after 1 second it will have reached the top of its "arch" and will then start back down. From there it will take about another 1.5 seconds to reach the ground, but since horizontal motion continues it will have stayed airborne for 2.5 seconds and in that time it will have covered about 70 feet!
The maximum distance is when the angle is 45 degrees.