Final answer:
The kinetic energy of the soccer ball at the apex of its trajectory is approximately 163.4 Joules, calculated using the horizontal component of the velocity which remains constant throughout the projectile's flight.
Step-by-step explanation:
To determine the kinetic energy of the soccer ball at the apex of its trajectory, we need to consider the properties of projectile motion. At the apex, the vertical component of the velocity is zero, and only the horizontal component remains. The initial velocity of the ball is given as 35.0 m/s at an angle of 38.0° to the horizontal. We can calculate the horizontal component (Vx) using the cosine function: Vx = V * cos(θ), where V is the initial velocity and θ is the angle of projection.
Vx = 35.0 m/s * cos(38.0°) ≈ 27.85 m/s
Once we have the horizontal component of the velocity, we can calculate the kinetic energy (KE) at the apex using the formula: KE = (1/2) * m * Vx², where m is the mass of the soccer ball.
KE = (1/2) * 0.420 kg * (27.85 m/s)² ≈ 163.4 Joules
Therefore, the kinetic energy of the soccer ball at the apex of its trajectory is approximately 163.4 Joules.