A Cyclist's Leap of Faith: Calculating Cliff Heights

When faced with the task of determining the height of a cliff that a cyclist jumped from, it may initially seem like a daunting challenge. However, by breaking down the problem into its component parts and applying the principles of physics, we can unveil the answer with confidence.

Horizontal Motion Analysis

Initially, let's focus on the horizontal component of the motion. Given that the cyclist jumps off horizontally, the horizontal velocity (vx) remains constant and is equal to the initial velocity of 18 m/s. To find the time in the air (t), we can use the equation t = d / vx, where d is the horizontal distance traveled before touching down, which is 16.6 m in this case.

Vertical Displacement Calculation

Next, we shift our attention to the vertical component of the motion. Since the initial motion is purely horizontal, the vertical component of the initial velocity (vy) is 0 m/s. By utilizing the kinematic equation h = vy × t + (1/2) × g × t², where g is the acceleration due to gravity (9.81 m/s²), we can calculate the vertical displacement. The height of the cliff is then determined to be approximately 4.18 m.