Question

Can a goalkeeper at her/ his goal kick a soccer ball into the opponent’s goal without the ball touching the ground? The distance will be about $\mathbf{95}\mathbf{m}$. A goalkeeper can give the ball a speed of $\mathbf{30}\mathbf{m}/\mathbf{s}$.

Short answer

No goalkeeper cannot goal kick a soccer ball into the opponent’s goal without the ball touching the ground

Step-by-step solution

Given data

The problem is asking us to calculate the range. If the initial velocity of the ball is 30 m/s. To maximum the range of the ball the angle should be kicked at 45 degree.

The formula of range is

$R_x=\frac{{V_i}^{2}sin\left(2{\theta }_i\right)}{g}$

Range of the ball

Putting the value of range in the equation

$\begin{array}{rcl}{R}_x& =& \frac{{V_i}^{2}sin\left(2{\theta }_i\right)}{g}\\ If \theta & =& 45\\ R_x& =& \frac{{\left(30\right)}^{2}sin\left(90\right)}{9.8}\\ R_x& =& 91.8 m\\ & & \end{array}$

The range of the ball is 91.8 meter, which is less 95 meter. No goalkeeper cannot goal kick a soccer ball into the opponent’s goal without the ball touching the ground.