Why is 45 degrees the maximum range?
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.
At what angle height is maximum?
The textbooks say that the maximum range for projectile motion (with no air resistance) is 45 degrees.
At what angle of projection height is maximum?
Complete step by step answer: If the angle of projection is 75.96∘, the maximum height is equal to the horizontal range.
What angle gives maximum time in the air?
Given the equations of projectile motion (no air resistance), it is easy to find the launching angle theta that produces the maximum range. That angle is 45 degrees. The maximum time of flight is obtain instead for a launching angle theta=90 degrees: the projectile is launched straight up and the range is zero.
Why does launch angle affect distance?
Launching slightly upward will increase the distance because the projectile travels for a longer time. But launching too close to straight up would decrease the distance, since the projectile has no horizontal velocity. 5.
Why do complementary angles give the same range?
They are equal because the sine value of 60 degrees is equal to the sine value of 120 degrees. Other complementary angles such as 20 degrees and 70 degrees will also confirm the equality of range 1 to range 2.
How can two angles have the same range?
Any two angles that have a 2:1 ratio will result in the same range when launched at the same speed. b. Two launch angles that add to 90° will result in the same range when launched at the same speed.
At what angles ranges are equal?
The horizontal distance traveled by a projectile is called its range . A projectile launched on level ground with an initial speed v0 at an angle θ above the horizontal… will have the same range as a projectile launched with an initial speed v0 at 90° − θ.
For which pair of angles is the range equal?
Horizontal range Horizontal range is same for a pair of projection angle. It means that the range of the projectile with a given initial velocity is same for a pair of projection angles θ and 90° – θ.
Why are ranges equal?
Two ranges are considered equal if they have the same number of elements and every pair of corresponding projected elements satisfies pred .
What is the relation between range and maximum height of θ 45?
Motion in A Plane. Prove that the maximum horizontal range is 4 times the maximum height attained by a projectile. The horizontal range is maximum when the angle of projection is 45°. That is, range is 4 times the maximum height attained by a projectile.
What is the relation between maximum height and horizontal range?
The initial velocity of the projectile is um/s, H is the maximum height of the projectile and R is its horizontal range. In the question, we are asked to find the angle of projection, i.e. θ. To find θ , let us divide the maximum height of the projectile by horizontal range. And sin2θ can be written as 2sinθcosθ.
Is the maximum height attained by projectile is largest when its horizontal range is maximum?
No , horizontal range is maximum when θ=45∘ and maximum heitht attained by projectile is largest when θ=90∘.
What is the relation between time of flight and maximum height?
The time of flight is just double the maximum-height time. At maximum height, vy = 0. The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.