How Far Apart Are Sam and Joe?
Based on the data, how far apart are Sam and Joe?
a. 18.51 meters
How long was the ball in the air?
b. 1.55 seconds
Final answer:
To find the distance between Sam and Joe, we need to find the horizontal component of the ball's initial velocity and multiply it by the time the ball is in the air. To find the time the ball is in the air, we can use the equation t = 2 * Vy / g. Finally, we can find the distance between Sam and Joe by substituting the values into the equation d = Vx * t.
Answer:
Sam and Joe are 18.51 meters apart based on the data given. The ball was in the air for 1.55 seconds before Joe caught it.
Explanation:
To find the distance between Sam and Joe, we need to split the ball's initial velocity into horizontal and vertical components. The horizontal component is given by the equation Vx = V * cos(theta), where V is the initial speed of the ball and theta is the angle of projection.
In this case, Vx = 14.3 m/s * cos(32.9) = 11.96 m/s. Since Sam and Joe are at the same height, the horizontal distance traveled by the ball is equal to the distance between Sam and Joe, which is given by the equation d = Vx * t, where t is the time the ball is in the air.
To find the time the ball is in the air, we can use the vertical component of its initial velocity, which is given by Vy = V * sin(theta).
In this case, Vy = 14.3 m/s * sin(32.9) = 7.6 m/s. The time the ball is in the air can be found using the equation t = 2 * Vy / g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the values, we get t = 2 * 7.6 m/s / 9.8 m/s^2 = 1.55 seconds. Finally, we can find the distance between Sam and Joe by substituting the values into the equation d = Vx * t. Therefore, Sam and Joe are 18.51 meters apart.