George drops a stone from atop a cliff of 25m. How long does it take to hit the ocean below, what velocity is it travelling when it gets there?
To find the time it takes for the stone to hit the ocean below and its velocity at that moment, we can use equations of motion and the principles of free fall.
1. Start by using the equation for the time it takes to fall under free fall:
💡 Time (t) = √(2h/g)
Where:
h = height (25m)
g = acceleration due to gravity (approximately 9.8 m/s²)
Plugging in the values, we have:
Time (t) = √(2 * 25 / 9.8)
Calculating this, t ≈ 2.53 seconds (rounded to two decimal places).
2. Now, let's find the final velocity (Vf) at the moment it hits the ocean surface. We can use the equation:
💡 Final velocity (Vf) = Initial velocity (Vi) + acceleration (a) * time (t)
Since the stone is dropped, Vi is zero (as it was not given any initial upward velocity).
Therefore,
Vf = 0 + 9.8 * 2.53
Calculating this, Vf ≈ 24.79 m/s (rounded to two decimal places).
So, it takes approximately 2.53 seconds for the stone to hit the ocean below, and its velocity at that moment is approximately 24.79 m/s.
To answer this question, we can use the laws of motion and equations of motion to find the time it takes for the stone to hit the ocean and the velocity at that moment. Let's break it down step by step:
Step 1: Determine the acceleration due to gravity
The acceleration due to gravity near the Earth's surface is approximately 9.8 m/s². We can assume the stone falls vertically downward, so the acceleration will be in the downward direction.
Step 2: Calculate the time it takes to hit the ocean
We can use the kinematic equation:
s = ut + (1/2)at²
where
s = distance (25m in this case, equivalent to the height of the cliff)
u = initial velocity (0 since the stone is dropped)
t = time taken
a = acceleration due to gravity (-9.8 m/s², taking a negative value since it's downward)
Plugging in the known values, we can solve for t:
25 = 0t + (1/2)(-9.8)t²
25 = -4.9t²
t² = -25 / -4.9
t² ≈ 5.1
t ≈ √5.1
t ≈ 2.3 seconds (approximated to one decimal place)
Therefore, it takes approximately 2.3 seconds for the stone to hit the ocean below.
Step 3: Calculate the velocity at the moment it hits the ocean
We can use another equation to find the final velocity (v) at the moment the stone hits the ocean:
v = u + at
where
v = final velocity
u = initial velocity (0 since the stone is dropped)
a = acceleration due to gravity (-9.8 m/s², taking a negative value since it's downward)
t = time taken (2.3 seconds)
Plugging in the values:
v = 0 + (-9.8)(2.3)
v ≈ -22.5 m/s
Therefore, the stone is traveling at approximately -22.5 m/s (negative sign indicates downward direction) when it hits the ocean below.
h = 0.5g*t^2.
h = 25 m., g = 9.8 m/s^2, t = ?.