A stone thrown horizontally from a height of 6.32 m hits the ground at a distance of 14.30 m. Calculate the speed of the stone as it hits the ground. Neglect air resistance.
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To calculate the speed of the stone as it hits the ground, we can make use of the equations of motion.
The given information about the stone's motion allows us to determine the time it takes for the stone to hit the ground.
First, let's calculate the time it takes for the stone to fall vertically from a height of 6.32 m using the formula:
s = ut + (1/2)at^2
where:
s = vertical displacement = 6.32 m (height of the stone)
u = initial velocity in the vertical direction = 0 m/s (as the stone is thrown horizontally)
a = acceleration in the vertical direction = 9.8 m/s^2 (acceleration due to gravity)
t = time
Since the stone is initially thrown horizontally, its initial velocity in the vertical direction (u) is 0 m/s.
6.32 = 0 * t + (1/2) * 9.8 * t^2
Simplifying the equation:
6.32 = 4.9t^2
Dividing both sides of the equation by 4.9:
t^2 = 6.32 / 4.9
t^2 ≈ 1.29
Taking the square root of both sides:
t ≈ √1.29
t ≈ 1.14 seconds
Now we know that it takes approximately 1.14 seconds for the stone to hit the ground.
To find the horizontal distance traveled by the stone, we can use the formula:
s = ut + (1/2)at^2
where:
s = horizontal displacement = 14.30 m
u = initial velocity in the horizontal direction = ?
a = acceleration in the horizontal direction = 0 m/s^2 (since there is no acceleration horizontally)
t = time = 1.14 seconds
Using the equation:
14.30 = u * 1.14 + (1/2) * 0 * (1.14)^2
Simplifying the equation:
14.30 = 1.14u
Dividing both sides of the equation by 1.14:
u ≈ 14.30 / 1.14
u ≈ 12.54 m/s
Therefore, the speed of the stone as it hits the ground is approximately 12.54 m/s.