can a goalkeeper at her/his goal kick a soccer ball into the opponents goal without the ball touching the…
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.\nyes\nno
Answer
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