Final answer:
It takes approximately 4.0 seconds for the stone to reach the bottom of the cliff when thrown horizontally with a velocity of 5.0 m/s from a height of 78.4 m, considering only the vertical motion due to gravity.
Step-by-step explanation:
The question at hand involves calculating the time it takes for a stone to reach the bottom of a cliff when thrown horizontally from its top. The stone is thrown with a horizontal velocity of 5.0 m/s from a height of 78.4 m. Since the stone is thrown horizontally, only the vertical motion needs to be considered to determine the time of flight because the horizontal and vertical motions are independent of each other.
To find the time, we use the equation for the vertical motion in free fall:
s = ut + ½at²
Where:
- s is the displacement (height of the cliff, which is 78.4 m)
- u is the initial vertical velocity (0 m/s, since it's thrown horizontally)
- a is the acceleration (9.81 m/s², due to gravity)
- t is the time, which we need to calculate
Inserting the values into the equation, we get:
78.4 = 0*t + ½*9.81*t²
The equation simplifies to:
78.4 = 4.905*t²
Dividing both sides by 4.905 gives:
t² = 15.98165
Taking the square root to solve for t gives:
t ≈ 4.0 seconds
So, the stone takes approximately 4.0 seconds to reach the bottom of the cliff.