Answer:Therefore, the ball clears the crossbar by a height of approximately 5.01 meters.
Step-by-step explanation:
To solve this problem, we can use the equations of motion for projectile motion.
First, we need to calculate the time of flight of the ball. We can use the vertical component of the initial velocity to find the time it takes for the ball to reach its maximum height, and then use that time to calculate the total time of flight.
Vertical component of initial velocity = 19 m/s * sin(42.3) = 12.7 m/s
We can use the formula:
time = vertical component of initial velocity / acceleration due to gravity
time = 12.7 m/s / 9.8 m/s^2 = 1.2959 seconds
The total time of flight will be twice this value, or 2.5918 seconds.
Next, we need to calculate the maximum height that the ball reaches. We can use the formula:
maximum height = (vertical component of initial velocity)^2 / (2 * acceleration due to gravity)
maximum height = (12.7 m/s)^2 / (2 * 9.8 m/s^2) = 8.1657 meters
Finally, we can calculate how much higher than the crossbar the ball will clear. We know that the ball must clear the crossbar by a height of:
crossbar height + ball radius = 3.05 m + 0.11 m = 3.16 m
Therefore, the vertical distance that the ball clears the crossbar is:
maximum height - (crossbar height + ball radius) = 8.1657 m - 3.16 m = 5.0057 meters
Therefore, the ball clears the crossbar by a height of approximately 5.01 meters.