Projectile Motion: Calculating Time Spent in the Air

Projectile motion is a fundamental concept in physics that involves the motion of objects projected into the air and affected by gravity. When analyzing the motion of a soccer ball, understanding the initial velocities is crucial to determining various parameters, including the time the ball spends in the air.

In the given scenario, the soccer ball is kicked with an initial resultant velocity of 10m/s and an initial horizontal velocity of 6.4m/s. To calculate the time the ball stays in the air, we need to separate the initial velocity into horizontal and vertical components.

The initial resultant velocity and horizontal velocity allow us to use Pythagoras' theorem to find the vertical component of the initial velocity. By determining the vertical velocity, we can then proceed to calculate the time spent in the air based on the vertical motion of the ball.

The formula to calculate the time in the air for a projectile is t = 2*v/g, where v represents the vertical initial velocity and g is the acceleration due to gravity (approximately 9.8 m/s²). By plugging in the calculated vertical velocity value, we can determine the time the soccer ball remains airborne.

It's important to note that in projectile motion, time is solely determined by the vertical motion of the object, disregarding factors such as air resistance. The higher the initial vertical velocity or altitude, the longer the object will stay in the air before landing.