That is, range is 4 times the maximum height attained by a projectile. In the question, we are asked to find the angle of projection, i. The time of flight is just double the maximum-height time. The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.
Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Physics Why is 45 degrees the maximum range?
Ben Davis February 10, Why is 45 degrees the maximum range? In any football game both teams square off against each other and against a shared opponent as well—gravity. Earth's gravitational pull makes long-range passing a challenge and pulls down even the hardest-struck punts and placekicks. Because gravity is a constant, experienced quarterbacks and kickers can account for its effects to move the ball downfield as efficiently as possible.
Like all projectiles, a football, once released, follows a path known in mathematical terms as a parabola—a symmetric arc that eventually returns the ball back to the ground. In real life a projectile's flight is affected not only by gravity but by wind and drag from air resistance, so the parabola would not be perfect. Parabolas have been studied for millennia, and their properties are well understood.
That may look like a complicated equation, but a couple of the variables can be ignored. First, because the force of gravity is constant, g will be the same no matter how a punter kicks the ball. What is the best angle for maximum height and air time? The best angle for maximum height is 90 o because the initial speed all goes into the vertical component to achieve the highest height. The best angle for air time is Vinyet Fisher Pundit. What is the best angle to throw a ball at for maximum range?
Most people know that a ball without air resistance traditional projectile motion goes the farthest if you throw it at a 45 degree angle. Janine Kinzkofer Pundit. What is the optimum launch angle for distance? Enaitz Santillan Pundit. How do you calculate projectile distance? Gennie Piasecki Pundit. How do you maximize projectile distance? Augustus Uhrmacher Pundit.
What is the formula for range of a projectile? The range R of the projectile is the horizontal distance it travels during the motion. Emerita Jeske Teacher. What is the best angle to launch a projectile? Kremena Iuhi Beginner. What is horizontal range? The only way to increase the jump distance D is to to increase the horizontal launch speed, V, by taking a long runup.
Actually, D is a bit larger than this because the feet land ahead of the centre of mass and because the centre of mass starts from a point in front of the feet at the start of the jump. In athletic events, there is another consideration. That is, the force that can be applied in the horizontal direction is not the same as the force that can be applied in the vertical direction.
A ball can be thrown faster in the horizontal direction than in the vertical direction. Consequently, the best launch angle for the shot put or the javelin throw is even lower than one might expect just from the aerodynamics of the problem. If a ball or any other object is moving at speed V through the air, then the air exerts a backwards force on the ball called the drag force.
If the ball is moving vertically up then the drag force acts vertically down and vice versa. If the ball is moving forward in a horizontal direction then the drag force acts backward in a horizontal direction. The formula for the drag force is. The value of d at 20 degrees Centigrade is 1. Unlike the gravity force, the drag force does not depend on the mass of the ball. It depends only on its radius and speed. C D depends to some extent on the surface roughness of the ball and it also depends on ball speed.
For a streamlined object, C D can be less than 0. The value of C D is constant and equal to about 0. The drag force itself may or may not drop when C D drops, since F is proportional to V squared.
The drop in C D occurs as a result of a change from smooth or laminar air flow around the ball to a more turbulent flow. The drop in C D is especially large on very smooth balls, is smaller on slightly rough balls and does not occur at all for a tennis ball since the ball surface is too rough. For a tennis ball, C D is about 0.
A fluffy ball will slow down faster, partly because the drag coefficient is larger and partly because the ball diameter is then larger. The speed at which C D drops depends on the diameter of the ball. It occurs at low ball speeds on large balls such as a soccer ball and at high ball speeds for small balls such as a golf ball. Golf balls are slightly dimpled so that C D drops at a lower ball speed than it would for a perfectly smooth ball.
For example, C D drops to about 0. For a golf ball, C D drops to about 0. However, if the ball is struck at 45 degrees then it will travel further in a vacuum than in air.
The effect of the drag force is very noticeable on balls or other objects that are relatively light. It is the drag force on a leaf or a piece of paper that causes it to take a longer time to fall to the ground than a heavy object. Most players would not even notice that the ball slows down as it travels through the air, but it does.
A ping-pong ball would not even make it over the net. The drag force on a ping-pong ball is less than that on a larger tennis ball travelling at the same speed, but the mass of a ping-pong ball is many times smaller and the drag force therefore has a much bigger effect in slowing it down. The effect of the drag force on a 20 cm diameter balloon dropped from the ceiling in my office is shown in Movie A.
For comparison, Movie B shows the same situation for a baseball dropped from the ceiling. It is obvious that the balloon falls much more slowly than the baseball. The acceleration of the baseball is essentially equal to 9. After falling through a height of 2.
It was relatively easy to calculate the drag coefficient for the balloon by measuring its speed as it fell. I wanted to check whether the drag coefficient was about 0.
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