To determine the maximum height reached by the ball, we need to calculate the time it takes for the ball to reach its peak and then use that time to find the height.
When the ball is thrown vertically, its initial velocity is 2 m/s, and the acceleration due to gravity causes it to decelerate at 10 m/s². The ball will eventually come to a stop at its peak before falling back down.
To find the time taken to reach the peak, we can use the equation:
v = u + at
Where: v = final velocity (0 m/s at the peak) u = initial velocity (2 m/s) a = acceleration (-10 m/s²) t = time
Rearranging the equation, we have:
t = (v - u) / a
Substituting the values, we get:
t = (0 - 2) / (-10) t = 2 / 10 t = 0.2 seconds
Now that we have the time taken to reach the peak, we can calculate the maximum height using the equation:
h = ut + (1/2)at²
Where: h = height u = initial velocity (2 m/s) t = time (0.2 seconds) a = acceleration (-10 m/s²)
Substituting the values, we have:
h = 2 * 0.2 + (1/2) * (-10) * (0.2)² h = 0.4 + (-1) * 0.04 h = 0.4 - 0.04 h = 0.36 meters
Therefore, the maximum height reached by the ball is 0.36 meters.