%IMG% (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 t...
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%IMG%
(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) 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 Rmax:
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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