(a) The diagram above illustrates a projectile motion. Identify each of the physical quantities labeled P, β, H and R. (b) Write an equation to show the rel...

(a) The diagram above illustrates a projectile motion. Identify each of the physical quantities labeled P, β, H and R.               

                                                 
(b) Write an equation to show the relationship between P, g and Rmax’ where g is the acceleration due to gravity and Rmax is maximum R.                    

Answer Details

(a)

• P represents the initial velocity of the projectile.
• β represents the angle of projection, which is the angle between the horizontal and the velocity vector of the projectile at the time of projection.
• H represents the maximum height reached by the projectile.
• R represents the range of the projectile, which is the horizontal distance covered by the projectile from its point of projection to the point where it lands.

(b)

The relationship between P, g, and R_max can be represented by the following equation:

R_max = (P²) * sin(2β) / g

This equation shows that the maximum range of a projectile depends on the initial velocity of the projectile (P), the acceleration due to gravity (g), and the angle of projection (β). The equation states that the maximum range is proportional to the square of the initial velocity and the sine of the double of the angle of projection. The sine function appears in the equation because it represents the vertical component of the velocity, which affects the height of the projectile and, in turn, the range.

In simple terms, this equation shows that the maximum range of a projectile can be increased by either increasing the initial velocity or by increasing the angle of projection, or by a combination of both.