# Why is a 45 degree angle the best trajectory?

## Why is a 45 degree angle the best trajectory?

As ball speed increases, so does the drag force and the lower is the required launch angle. A launch at 45 degrees would allow the ball to remain in the air for a longer time, but it would then be launched at a lower horizontal speed at the start and it would slow down more because of the longer flight time.

How do you find the maximum distance of a projectile?

The equation for the distance traveled by a projectile being affected by gravity is sin(2θ)v2/g, where θ is the angle, v is the initial velocity and g is acceleration due to gravity. Assuming that v2/g is constant, the greatest distance will be when sin(2θ) is at its maximum, which is when 2θ = 90 degrees.

For what angle of projection height is maximum?

As you can see from the figure, the larger the initial launch angle, the closer the object comes to maximum height and the longer the flight time. The largest range will be experienced at a launch angle up to 45 degrees.

### What is maximum range of a projectile?

The textbooks say that the maximum range for projectile motion (with no air resistance) is 45 degrees.

What is the best angle for maximum range?

45°
For ideal projectile motion, which starts and ends at the same height, maximum range is achieved when the firing angle is 45°. If air resistance is taken into account, the optimal angle is somewhat less than 45° and this is often considered obvious.

What is maximum range in projectile motion?

#### How does angle affect the range of a projectile?

The highest point in the trajectory occurs at the midpoint of the path. This highest point increases as the angle increases. The range is also the same for a 30° and a 60° launch angle. As a final example, the range is the same for a 40° and a 50° launch angle.

What is the formula of maximum height in projectile motion?

h = v 0 y 2 2 g . This equation defines the maximum height of a projectile above its launch position and it depends only on the vertical component of the initial velocity.

What is the angle of projection of projectile for which its maximum height and horizontal range are equal?

If the angle of projection is \[{75.96^ \circ }\], the maximum height is equal to the horizontal range.

## What is the optimal angle for projectile motion?

What is the range of projectile motion?

The range of the projectile is the displacement in the horizontal direction. There is no acceleration in this direction since gravity only acts vertically. shows the line of range. Like time of flight and maximum height, the range of the projectile is a function of initial speed.

What angle does a projectile travel the farthest?

A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees. But what about trying to maximize a projectile’s height to increase hang time?

### Which launch angle will go the farthest?

You can also turn the equation around to find maximum height: The 45° launch angle will go the farthest distance. Why? The 45° angle goes the farthest because it provides both a long time for the dart to be in the air and constant enough horizontal speed.

What is the launch angle of a projectile at 30 degrees?

Projectile Motion CHECK YOUR ANSWER, Continued-1 Neglecting air drag, a ball tossed at an angle of 30with the ° horizontal will go as far downrange as one that is tossed at the same speed at an angle of. B. 60° Explanation: Same initial-speed projectiles have the same range when their launching angles add up to 90° .

How do you calculate projectile motion without air resistance?

When calculating projectile motion, you won’t take air resistance into account to make your calculations simpler. Rather than using the projectile motion equations to find the projectile motion, you can use the projectile motion calculator which is also known as horizontal distance calculator, maximum height calculator or kinematic calculator.