A stone is thrown horizontally from a cliff 25m high and lands on the ground 22 m from the foot of the cliff. What is the horizontal acceleration on the stone?
To find the horizontal acceleration on the stone, we first need to understand the motion of the stone.
Given that the stone is thrown horizontally, it means that its initial vertical velocity is 0 m/s. The only force acting on it in the vertical direction is gravity, which causes it to accelerate downward at a rate of 9.8 m/s^2.
Since the stone lands on the ground, it takes some time to reach the horizontal distance of 22 m. We need to find the time it takes for the stone to fall to the ground.
Using the equation:
d = v * t + (1/2) * a * t^2
where:
d = vertical distance (25 m)
v = initial vertical velocity (0 m/s)
t = time taken
a = vertical acceleration (-9.8 m/s^2)
Putting the values in, we have:
25 = 0 * t + (1/2) * (-9.8) * t^2
Simplifying the equation, we get:
25 = -4.9 * t^2
Dividing both sides of the equation by -4.9, we have:
t^2 = -25 / -4.9
Taking the square root of both sides, we get:
t = √(25 / 4.9) ≈ 2.03 s
Now that we know the time it takes for the stone to reach the ground, we can find the horizontal acceleration using the equation:
a = d / t
where:
a = horizontal acceleration
d = horizontal distance (22 m)
t = time taken (2.03 s)
Putting the values in, we have:
a = 22 / 2.03
Simplifying the equation, we get:
a ≈ 10.84 m/s^2
Therefore, the horizontal acceleration on the stone is approximately 10.84 m/s^2.