Final answer:
To find the distance from the base of the cliff where the motorcycle will land, use the equations of projectile motion. The motorcycle will land approximately 139.8 m from the base of the cliff.
Step-by-step explanation:
To find the distance from the base of the cliff where the motorcycle will land, we can use the equations of projectile motion.
First, let's find the time it takes for the motorcycle to hit the ground. We can use the equation:
d = v0t + (1/2)at2
Where d is the vertical distance (22 m), v0 is the initial vertical velocity (0 m/s), t is the time in seconds, and a is the acceleration due to gravity (-9.8 m/s2).
Plugging in the values, we get:
22 = 0(t) + (1/2)(-9.8)(t2)
Simplifying, we find that t = √(2d/a) = √(2 * 22 / 9.8) ≈ 2.15 s
Now, we can find the horizontal distance using the equation:
d = vxt
Where d is the horizontal distance, vx is the horizontal velocity, and t is the time in seconds. Since there is no horizontal force acting on the motorcycle, its horizontal velocity remains the same, which is given as 65 m/s.
Plugging in the values, we get:
d = (65)(2.15) ≈ 139.8 m
Therefore, the motorcycle will land approximately 139.8 m from the base of the cliff.