To find the distance the soccer ball travels through the air, we can use the range formula for projectile motion. The range is the horizontal distance covered by the object. Here's how you can calculate it:
Convert the initial velocity from mph to m/s. 30 mph = 30 * 0.44704 m/s ≈ 13.4112 m/s
Resolve the initial velocity into horizontal and vertical components. The horizontal component remains constant throughout the motion and can be calculated as: horizontal component of velocity = initial velocity * cos(angle) horizontal component of velocity = 13.4112 m/s * cos(15 degrees)
Calculate the time of flight. The time it takes for the object to reach the ground can be determined using the vertical component of the velocity and the acceleration due to gravity. The vertical component of velocity is given by: vertical component of velocity = initial velocity * sin(angle) vertical component of velocity = 13.4112 m/s * sin(15 degrees)
Using the formula: time of flight = (2 * vertical component of velocity) / (acceleration due to gravity) time of flight = (2 * vertical component of velocity) / 9.8 m/s²
Calculate the horizontal distance traveled by the ball, which is the range. The formula is: range = horizontal component of velocity * time of flight
Now, we can plug in the values and calculate the distance:
horizontal component of velocity = 13.4112 m/s * cos(15 degrees) vertical component of velocity = 13.4112 m/s * sin(15 degrees) time of flight = (2 * vertical component of velocity) / 9.8 m/s² range = horizontal component of velocity * time of flight
After calculating these values, you will have the distance the soccer ball travels through the air.