Final answer:
To solve the physics problem, use the kinematic equation d = 1/2 * g * t² to find the time it takes for the rock to hit the ground and then calculate the horizontal displacement with s = v * t, using the constant horizontal velocity and the time of flight.
Step-by-step explanation:
You are asking about the motion of a rock thrown horizontally from the top of a cliff. This question involves two parts: (a) determining the time it takes for the rock to reach the ground, and (b) finding the horizontal displacement of the rock at the moment it impacts the ground. Let's address each part separately.
Time to reach the ground:
To find out how long the rock takes to reach the ground, we can use the kinematic equation for uniformly accelerated motion along the vertical axis, assuming the only acceleration is due to gravity (9.81 m/s²). Since the rock is thrown horizontally, its initial vertical velocity is 0 m/s.
The kinematic equation we use is:
d = 1/2 * g * t²
where d is the vertical distance (the height of the cliff), g is the acceleration due to gravity, and t is the time in seconds. Solving for t gives us the time it takes the rock to fall 122.5 meters.
Horizontal displacement:
The horizontal displacement can be determined by the horizontal speed of the rock and the time it is in the air (which we found from the first part). The horizontal speed remains constant, as there is no acceleration in the horizontal direction (ignoring air resistance). The formula is:
s = v * t
where s is the horizontal displacement, v is the horizontal velocity (10.0 m/s), and t is the time it has been in the air.
Once the time t is computed from the first part, we can easily find the horizontal displacement by multiplying it by the constant horizontal velocity.