To solve this problem, we can use the equations of motion to determine the horizontal distance traveled by the stone before it strikes the ground.
We know that the stone is thrown horizontally with an initial velocity of 10 m/s. In the horizontal direction, there is no acceleration acting on the stone. Therefore, the horizontal component of the stone's velocity remains constant throughout its motion.
The horizontal distance traveled by the stone can be calculated using the equation:
Distance = Velocity × Time
Since the stone is thrown horizontally, the initial vertical velocity is 0 m/s. The only force acting on the stone in the vertical direction is gravity, causing it to accelerate downward at a rate of 9.8 m/s².
To calculate the time it takes for the stone to reach the ground, we can use the equation:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time²)
In this case, the initial vertical velocity is 0 m/s, the acceleration is -9.8 m/s² (negative because it acts downward), and the distance is 80 m (height of the cliff). We need to solve for time.
80 = 0 + (0.5 × -9.8 × Time²)
Simplifying the equation:
80 = -4.9 × Time²
Dividing both sides by -4.9:
Time² = -80 / -4.9
Time² = 16.3265
Taking the square root:
Time = √16.3265
Time ≈ 4.04 seconds (rounded to two decimal places)
Now that we know the time it takes for the stone to reach the ground, we can calculate the horizontal distance traveled:
Distance = Velocity × Time Distance = 10 m/s × 4.04 s Distance ≈ 40.4 meters (rounded to one decimal place)
Therefore, the stone will strike the ground approximately 40.4 meters away from the base of the cliff.