A soccer ball is kicked at an angle of 30° to the horizontal with an initial velocity of 16 m/s. How far does the soccer ball go?
3.8
To determine how far the soccer ball goes, we can use the equations of projectile motion. The horizontal and vertical motion of the ball can be analyzed separately.
First, let's find the time it takes for the ball to reach the highest point of its trajectory. The initial velocity in the vertical direction can be found using trigonometry:
Initial vertical velocity (Vy) = Initial velocity (16 m/s) * sin(angle of 30°)
The time taken to reach the highest point can be found using the equation:
Time to reach highest point (t) = Vy / gravitational acceleration
(Note: gravitational acceleration is approximately -9.8 m/s^2)
Next, we can find the total time of flight by doubling the time to reach the highest point:
Total time of flight (T) = 2t
Now, let's calculate the horizontal distance traveled by the ball. The horizontal velocity remains constant throughout the motion:
Horizontal velocity (Vx) = Initial velocity (16 m/s) * cos(angle of 30°)
The horizontal distance (D) can be calculated by multiplying the horizontal velocity by the total time of flight:
Distance (D) = Vx * T
Using these equations and calculations, we can find the distance the soccer ball travels.