Question

In the javelin throw, hammer throw, or discus, the goal is maximum distance. Ignoring air resistance and the athlete’s biomechanics, at what angle should the athlete throw these objects to maximize the distance they travel before hitting the ground

Answer 1

First, remember the equation that describes the range of an object launched at some angle without air resistance:

$$R=\frac{u^2\text{sin}(2\theta)}{g}.$$

We need maximum range at given initial velocity $u$. Thus, the only variable we can change is theta, the angle. The angle changes the sine function. Also, we know that the maximum value of a sine function is 1, which occurs at 90°. So, the argument is $2\theta$, which gives

$$2\theta=90°,\\ \theta=45°.$$

At 45° the range will be maximum.