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Suppose the projective is launched, over a level surface, with initial velocity u, which makes an angle x with the horizontal. Then 0 <= x <= 90 degrees.Ignore the effects of all forces other than gravity,
Ananlyse the motion in the vertical direction.
The vertical component of u is u*sin(x), and the projectile is in the air until its vertical displacement returns to 0.
That is t is given by
0 = u*sin(x)*t - 1/2*g*t^2 where g is the acceleration due to gravity.
ie 0 = t*{u*sin(x) - 1*2*g*t}
that is t = 0 or u*sin(x) - 1/2*g*t
ignoring t = 0 since that is the initial position,
t = 2*u*sin(x)/g.
Now consider the horizontal motion.
The horizontal component of the initial velocity is u*cos(x) and [since we have chosen to ignore aerodynamic drag], this is a constant.
Therefore, horizontal distance covered in t units of time = u*cos(x)*t units of length.
Substituting for t gives
range = u*cos(x)*2*u*sin(x)/g = (u^2/g)*2*cos(x)*sin(x)
= c*2*cos(x)*sin(x) where c is a constant
= c*sin(2x) [using the double angle formula].
Now d(range)/dx = 2c*cos(2x) must be 0 at the maximum.
[It cannot be the minimum since x = 90 degrees gives a minimum range of 0].
therefore cos(2x) = 0
therefore 2x = 90 degrees and so x = 45 degrees.
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What projectile angle will get you the longest distance?
The optimal launch angle for the longest distance of a projectile is 45 degrees in the absence of air resistance. This angle allows for the greatest horizontal distance because it balances the vertical and horizontal components of the projectile's velocity.
The range of projectile is maximum when the angle of projection is?
The range of projectile is maximum when the angle of projection is 45 Degrees.
What is Trajectory?
A trajectory is the angle made with the horizontal when a projectile is fired. Suppose the projectile is a cannon ball. Assuming air is frictionless, that cannon ball will travel the greatest distance if the trajectory is 45 degrees from horizontal.
Does a projectile's distance covered decrease when fired at an angle above forty-five degrees?
The optimal angle to fire a projectile if the objective is distance is 45 degrees. It follows that the distance traveled decreases whether the angle is increased or decreased from 45.
A projectile upward at an angle of 75degree from the horizontal and strikes the ground a certain distance down range.For what other angle of launch ath the same speed wouldthis projectile land just a?
For the projectile to land at the same distance with the same initial speed, it must be launched at an angle of 15 degrees from the horizontal. This is because the range of a projectile is maximized when launched at a 45-degree angle. So, launching at 15 degrees in the opposite direction of 75 degrees should bring the projectile to the same landing point.
What is half projectile?
A half projectile refers to the projectile motion of an object where it is launched at an angle of 45 degrees to the horizontal. This angle maximizes the range of the projectile for a given initial velocity, making it travel the furthest distance before hitting the ground. The path of the projectile is a parabolic curve.
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The launch angle that results in the longest range for a projectile, in the absence of air resistance, is 45 degrees.
The angle of projection of a projectile for which the horizontal range and maximum height are equal?
45 degrees.
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The maximum height of a projectile depends on its initial velocity and launch angle. In ideal conditions, the maximum height occurs when the launch angle is 45 degrees, reaching a height equal to half the maximum range of the projectile.
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Without considering any effects of air resistance and wind, the angle of projection that delivers the greatest horizontal range is 45 degrees above the horizon. Anything different ... either more or less than 45 degrees ... reduces the range.
What is the greatest number of degrees in an obtuse angle?
179 degrees
What is the maximum angle needed to have a longest range in projectile motion?
45 degrees is the furthest one
