Question

can a goalkeeper at her/his goal kick a soccer ball into the opponents goal without the ball touching the ground? the distance will be about 95 m. a goalkeeper can give the ball a speed of 28 m/s.
yes
no

Explanation:

Step1: Analyze the motion as projectile

The motion of the soccer - ball is a projectile motion. The range formula for a projectile launched with initial speed \(v_0\) at an angle \(\theta\) is \(R=\frac{v_0^{2}\sin2\theta}{g}\), where \(v_0\) is the initial velocity, \(g = 9.8\ m/s^{2}\) is the acceleration due to gravity, and \(R\) is the range.

Step2: Find the maximum range

The function \(y = \sin2\theta\) has a maximum value of 1 when \(2\theta=90^{\circ}\) or \(\theta = 45^{\circ}\). Given \(v_0 = 28\ m/s\) and \(g=9.8\ m/s^{2}\), we substitute into the range formula.
\[R=\frac{v_0^{2}\sin2\theta}{g}\]
When \(\sin2\theta = 1\), we have \(R=\frac{v_0^{2}}{g}\). Substituting \(v_0 = 28\ m/s\) and \(g = 9.8\ m/s^{2}\), we get \(R=\frac{(28)^{2}}{9.8}=\frac{784}{9.8}=80\ m\).

Answer:

No