(a) State two objects each used in sports and warfare which may be considered as projectiles. (b) the horizontal range R, of a projectile is given by the ex...
Question 1 Report
(a) State two objects each used in sports and warfare which may be considered as projectiles.
(b) the horizontal range R, of a projectile is given by the expression;
R = \(\frac{u^2 sin 2\theta}{g}\) where \(\theta\) is the angle of projection, g the acceleration of free fall due to gravity and u the initial velocity. At what value of \(\theta\) will R be maximium?
Answer Details
(a) Objects that behave as projectiles
- In sports: a thrown javelin, a kicked football (also a shot-put, discus, or golf ball).
- In warfare: a bullet fired from a gun, a launched bomb or missile (also a cannon ball or arrow).
(b) Angle for maximum range
The range is \[ R = \frac{u^2 \sin 2\theta}{g} \] For a fixed initial speed u and fixed g, R is greatest when \(\sin 2\theta\) is greatest. The maximum value of a sine function is 1, so \[ \sin 2\theta = 1 \Rightarrow 2\theta = 90^{\circ} \Rightarrow \theta = 45^{\circ} \]
The range is maximum when the angle of projection is 45°.
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