Question

Projectile motion Importance of recognizing projectile motion in terms of enhancing one's performance in particular sport (basketball) As well as of how principles are work

Answer 1

When we throw a particle with some angle with respect to the horizontal the only force acting on the particle (after we throw it) is the force of gravity, we know that this force points down towards the center of the earth which, by Newton's second law that:

`\begin{gathered} ma=-mg \\ a=-g \end{gathered}`

That os, the particle is accelerating in the negative direction with a constant acceleration equal to the acceleration of gravity. Now, since the acceleration is only pointing in the y-direction we conclude the following:

• The horizontal motion has constant speed and, for this reason, it can be described as a uniform rectilinear motion.

,

• The vertical motion is a uniformly accelerated motion.

This means that we can described the position of the particle in each direction by the equations:

`\begin{gathered} x=x_0+v_(0x)t \\ y=y_0+v_(0y)t-(1)/(2)gt^2 \end{gathered}`

This type of motion is what we call a projectile motion. It turns out that a projectile motion is described, geometrically, by a vertical parabola that opens down; to prove it we solve t from the first equation:

`\begin{gathered} x=x_0+v_(0x)t \\ v_(0x)t=x-x_0 \\ t=(x-x_0)/(v_(0x)) \end{gathered}`

and we plug the value of t in the equation for the y position:

`y=y_0+v_(0y)((x-x_0)/(v_(0x)))-(1)/(2)g((x-x_0)/(v_(0x)))^2`

But we notice that this is a quadratic expression on x, which means that the trajectory of the motion is that of a parabola.

Now, this is the type of motion a basketball will follow once a player throws the ball into the air; this comes from the fact that the only force acting on the ball once it is thrown is its weight and then the analysis we made apply to the ball.