Final answer:
To find out how far from the base of the cliff the ball will land, first calculate the time for the ball to fall 45 meters using the vertical motion equation, and then use this time to calculate the horizontal distance with constant horizontal velocity of 20 m/s.
Step-by-step explanation:
The question pertains to the kinematics of a projectile in a physics context, specifically involving calculation of the horizontal distance traveled by a ball thrown from a height. Since the motion is horizontal and the only acceleration acting on the ball is due to gravity, we can separately analyze the horizontal and vertical motions.
To find the time it takes for the ball to fall 45 meters, we use the formula for the distance traveled under constant acceleration, which in this case is due to gravity: d = 1/2 * g * t^2, where d is the vertical distance, g is the acceleration due to gravity (9.8 m/s^2), and t is the time in seconds. With d = 45 m, we can solve for t.
Once we know the time t, we can calculate the horizontal distance traveled by the ball using the formula for horizontal motion at constant velocity: horizontal distance = horizontal velocity * time. The horizontal velocity remains constant at 20 m/s since we are ignoring air resistance.
First, calculate the time t, which is the square root of (2 * d / g), and plug in the values: t = sqrt(2 * 45 m / 9.8 m/s^2). Then find the horizontal distance with horizontal distance = 20 m/s * t.