Final answer:
To find the height of the cliff, we need to determine the vertical component of the initial velocity and use the equation for vertical displacement. The height of the cliff is approximately 44.65 meters.
Step-by-step explanation:
To find the height of the cliff, we can use the equations of motion for projectiles. Since the ball is launched at an angle of 60° above the horizontal, we can break down its initial velocity into horizontal and vertical components. The vertical component will give us information about the height of the cliff.
The initial velocity in the vertical direction can be found using the formula: Vy = V * sin(θ) where Vy is the vertical component of velocity, V is the initial velocity of the ball, and θ is the launch angle.
Substituting the given values, we have: Vy = 34 m/s * sin(60°) = 29.4 m/s.
Now, we can use the equation for vertical displacement: d = (Vy² - Vo²) / (2 * g) where d is the displacement, Vy is the final vertical component of velocity (which is 0 since the ball lands on the edge of the cliff), Vo is the initial vertical component of velocity, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values, we have: d = (0 - 29.4²) / (2 * 9.8) = -44.65 m.
Since the displacement is negative, it means the cliff is 44.65 meters high.