To find the total distance achieved by the ball, we need to consider its motion both during the upward journey and the subsequent downward journey.
During the upward journey, the ball slows down due to the opposing force of gravity until it reaches its highest point and starts to descend. The distance covered during the upward journey is equal to the distance covered during the downward journey.
Let's calculate the time taken for the ball to reach its highest point. We can use the following equation of motion:
v = u + at,
where: v = final velocity (which is 0 m/s at the highest point), u = initial velocity (30 m/s), a = acceleration due to gravity (-9.8 m/s²), and t = time taken.
Rearranging the equation, we have:
t = (v - u) / a.
Substituting the values, we get:
t = (0 - 30) / -9.8 t = 3.06 seconds (rounded to two decimal places).
The time taken for the upward journey is equal to the time taken for the downward journey.
To calculate the total distance, we'll use the equation of motion for distance:
s = ut + (1/2)at²,
where: s = total distance covered, u = initial velocity (30 m/s), t = total time taken (2 * 3.06 seconds), a = acceleration due to gravity (-9.8 m/s²).
Substituting the values, we get:
s = 30 * (2 * 3.06) + (1/2) * (-9.8) * (2 * 3.06)² s = 183.6 meters (rounded to one decimal place).
Therefore, the total distance achieved by the ball is approximately 183.6 meters.