What is the condition for maximum range of a projectile?

What is the condition for maximum range of a projectile?

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

How do you maximize the range of a projectile?

To maximize the range with respect to the firing angle θ we differentiate R with respect to θ and set this equal to 0. g 2 ∙ cos 2θ ( ) ∙ 0 therefore 2θ π 2 from which we obtain θ π 4 or 45 degrees. Suppose now we fire the projectile up a ramp which makes an angle α with respect to the horizontal.

What are the conditions of projectile motion?

A projectile is an object upon which the only force is gravity. Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity.

Which two factors will maximize the range of a projectile?

Range depends upon two factors, horizontal velocity and air time of the projectile. Since velocity was constant throughout the investigation, the only factor that had an impact upon the range is air time. Increasing the height means that the projectile has a greater vertical distance to travel.

What is the condition for maximum range of projectile and what is expression for maximum range?

Range of a Projectile Motion Equation 2 shows that for a given projectile velocity vo, R is maximum when sin2θo is maximum, i.e. when θo=45o.

What is mean by maximum horizontal range for a projectile What are the factors that depend on it?

The horizontal distance depends on two factors: the horizontal speed (vox) and the time the projectile has been in the air. The horizontal distance is the product of these two quantities. The height of the projectile depends on the original vertical speed (voy) and the time that the projectile has been in the air.

Why does 45 degrees give maximum range of a projectile?

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.

What are the condition to obtain maximum horizontal range?

Condition for the maximum horizontal range. The horizontal range isR will be maximum whenThus horizontal range is maximum when it is projected at an angle of 45o with the horizontal e.g. if a long jumper take off at an angle 45o he will cover the maximum horizontal range.