Final answer:
To calculate the height of the cliff, use the equation for vertical displacement: Δy = V₀y * t + 0.5 * g * t². Since the ball is thrown 45 degrees above the horizontal, use the equation V₀y = V₀ * sin(theta) to find the initial vertical velocity. Substituting the values into the equations gives a height of approximately 106.9 meters.
Step-by-step explanation:
To calculate the height of the cliff, we can use the equation for vertical displacement:
Δy = V₀y * t + 0.5 * g * t²
Where Δy is the vertical displacement, V₀y is the initial vertical velocity, t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Since the ball is thrown 45 degrees above the horizontal, the initial vertical velocity can be found using the equation:
V₀y = V₀ * sin(theta)
Where V₀ is the initial speed of the ball (30 m/s) and theta is the launch angle (45 degrees).
After substituting the values into the equations and solving for Δy, we find that the height of the cliff is approximately 106.9 meters.