Question

formula 2 points a soccer ball is kicked at an angle of 60 degrees to the horizontal. the ball leaves the soccer players foot at 23.6 m/s, and takes a parabolic trajectory before landing on the ground. what is the velocity of the ball at the apex of the trajectory? answer

Explanation:

Step1: Resolve initial velocity into components

The initial velocity $v_0 = 23.6$ m/s. The horizontal - component of the initial velocity is $v_{0x}=v_0\cos\theta$ and the vertical - component is $v_{0y}=v_0\sin\theta$, where $\theta = 60^{\circ}$.
$v_{0x}=23.6\cos60^{\circ}=23.6\times\frac{1}{2}=11.8$ m/s, $v_{0y}=23.6\sin60^{\circ}=23.6\times\frac{\sqrt{3}}{2}\approx20.4$ m/s.

Step2: Analyze velocity at the apex

At the apex of the parabolic trajectory of a projectile, the vertical component of the velocity is zero ($v_y = 0$), and the horizontal component of the velocity remains constant throughout the motion because there is no acceleration in the horizontal direction (neglecting air - resistance).
So the velocity of the ball at the apex is equal to the horizontal component of the initial velocity.

Answer:

$11.8$ m/s