Final answer:
To calculate the height of the cliff, use the kinematic equation. Then, use the time of flight to find the horizontal distance. The stone's speed just before it hits the ground can also be calculated.
Step-by-step explanation:
To solve this problem, we can break it down into two parts - horizontal motion and vertical motion.
Horizontal Motion:
Since the stone is thrown horizontally, there is no acceleration in the horizontal direction. Therefore, the stone will continue to move with a constant velocity of 25.0 m/s horizontally until it hits the ground.
Vertical Motion:
We can use the kinematic equation to solve for the height of the cliff.
h = (vf^2 - vi^2)/(2g)
where h is the height of the cliff, vf is the final vertical velocity (which is 0 m/s since the stone hits the ground), vi is the initial vertical velocity (which can be calculated using the initial velocity and the launch angle), and g is the acceleration due to gravity (9.8 m/s^2).
Once we find the height of the cliff, we can use the time of flight to calculate the horizontal distance traveled.
d = vi * t
where d is the horizontal distance, vi is the initial horizontal velocity (which can be calculated using the initial velocity and the launch angle), and t is the time of flight.
Answer:
a) The height of the cliff is 45.9 meters. b) The stone lands approximately 73.3 meters from the foot of the cliff. c) The stone is moving at a speed of 31.1 m/s just before it hits the ground.