How Far Will Noah Jump from a 65-Foot Cliff with Initial Horizontal Velocity of 6 m/s?

Noah wants to calculate the horizontal distance of his jump from a 65-foot cliff if he takes off with a horizontal velocity of 6 m/s. To resolve this, we can use the principles of projectile motion. First, we need to find the time it will take for Noah to fall the 65 feet (which needs to be converted to meters: 65 feet = 19.812 meters). Assuming there is no air resistance, the only acceleration Noah would experience would be due to gravity (9.8 m/s²).

Using the kinematic equation h = (1/2)gt², where h is the height (19.812 m) and g is the acceleration due to gravity, we can solve for t, the time in seconds: 19.812 m = (1/2)(9.8 m/s²)(t²). Solving for t gives us approximately 2.01 seconds.

Now, since horizontal motion is unaffected by gravity, and Noah's horizontal velocity is constant at 6 m/s, we can use the equation for horizontal distance, x = vt, where v is the velocity and t is the time. Therefore, the horizontal distance (x) Noah travels is: x = (6 m/s)(2.01 s) = 12.06 m. Thus, Noah's jump carries him a horizontal distance of approximately 12.06 meters.