The Maximum Height Reached by a Ball in Projectile Motion

Understanding Projectile Motion

In a typical projectile motion scenario, a child kicks a ball with an initial velocity of 8.5 m/s at an angle of 35° above the horizontal. The ball has an initial vertical velocity of 4.9 m/s and a total time of flight of 1.0 second. In this particular case, air resistance is neglected.

Calculating the Maximum Height

To determine the maximum height reached by the ball, we need to analyze the motion using fundamental physics principles and equations. The key factor to consider is the initial vertical velocity of the ball, which influences the time spent in the air.

At the highest point of the ball's flight, its vertical velocity momentarily reaches zero. This crucial point can be calculated using the equation of motion: v = u - gt, where 'v' is the final vertical velocity (0 at the highest point), 'u' is the initial vertical velocity, 'g' is the acceleration due to gravity (-9.8 m/s²), and 't' is the time taken to reach the highest point.

By solving for time 't', we find that t = 0.5 seconds, which represents the total time during which the ball is rising. The maximum height 'h' can then be determined using the equation: h = ut + 0.5 * g * t². Substituting the values, we calculate the maximum height reached by the ball to be approximately 1.2 meters.