Final answer:
To solve for the height of a cliff in a projectile motion problem, calculate the vertical component of the initial velocity and then use the kinematic equation for vertical motion with the given time.
Step-by-step explanation:
To calculate the height of the cliff in the question where a ball is thrown toward a cliff with a given initial speed and angle, we can use the projectile motion equations. Since the ball lands on the edge of the cliff after 4.41 seconds, we have enough information to determine the height (h) of the cliff.
To find the height, we need to calculate the vertical component of the ball's initial velocity using the equation Vy = V*sin(θ), where V is the initial speed and θ is the angle of projection. Then, we apply the kinematic equation for vertical motion h = Vy*t - (1/2)*g*t², where g is the acceleration due to gravity (9.81 m/s²), and t is the time the ball is in the air.
Given that the initial speed is 22.66 m/s and the angle of projection is 64°, the vertical component of the initial velocity Vy can be calculated. Then, by plugging Vy and t (4.41 s) into the kinematic equation, we can solve for the height h of the cliff.