%IMG% (a) The diagram above illustrates a... | WAEC SSCE - Physics - 2019 (Essay)

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(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

(a) Identifying the labelled quantities (standard projectile diagram):

P is the velocity of projection (the initial speed with which the body is launched).
β is the angle of projection (the angle the initial velocity makes with the horizontal).
H is the maximum height reached by the projectile.
R is the horizontal range (the horizontal distance travelled before the projectile returns to the launch level).

(b) Relationship between P, g and R_max:

The range of a projectile launched at speed \(P\) and angle \(\beta\) is

\[ R = \frac{P^{2}\sin 2\beta}{g}. \]

The range is greatest when \(\sin 2\beta = 1\), i.e. when \(\beta = 45^{\circ}\). Then

\[ R_{max} = \frac{P^{2}}{g}. \]

Equivalently, \(P = \sqrt{g\,R_{max}}\).

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