In the Disney movie Frozen, Anna and Kristoff find themselves in a tricky situation. They have to make a jump from a height of 200 feet, hoping to land safely in a pile of snow. But is surviving such a fall really possible?
Understanding Freefall
Before we answer this question, we need to understand what freefall means. When something is in freefall, it is falling under the force of gravity alone. This means that there is no other force acting upon it, such as lift, drag or air resistance.
Without any air resistance, an object falls at a constant acceleration of 9.8 m/s². This acceleration is known as the acceleration due to gravity or simply, g.
The Physics of a Freefall
The speed at which an object falls depends on how long it has been falling for, and the acceleration due to gravity. We can calculate this using the following formula for freefall:
v = gt
Here, v is the final velocity of the object, g is the acceleration due to gravity and t is the time for which the object has been falling.
For example, if a person jumps from a height of 100 feet (about 30 meters), the time it takes them to hit the ground is:
t = sqrt(2h/g)
Here, h is the height of the jump. Plugging in the values, we get:
t = sqrt(2 x 30 / 9.8) = 2.44 seconds
So, it takes about 2.44 seconds for a person to hit the ground after jumping from a height of 100 feet.
The Impact of Landing
Now, let’s consider what happens when a person lands on the ground after a jump. The force of the impact of the fall is known as the impact force, which depends on the mass and velocity of the object. The formula for impact force is:
F = ma
Here, F is the impact force, m is the mass of the object and a is the acceleration due to the impact. In the case of a person landing on the ground after a fall, the acceleration due to impact is the same as the acceleration due to gravity, but in the opposite direction.
Let’s consider a person who weighs 70 kilograms falling from a height of 100 feet (about 30 meters) and hitting the ground. The velocity at which they hit the ground can be calculated as:
v = gt
v = 9.8 x 2.44 = 23.91 m/s
The impact force can be calculated as:
F = ma
F = 70 x 9.8 = 686 N
This is equivalent to the force that a 70-kilogram object experiences when it is accelerated at a rate of 9.8 m/s². The impact of such a force can be very dangerous, and can easily result in broken bones, internal injuries or even death.
What Happens When You Land on Snow?
The impact force of a fall can be reduced if the falling object lands on a soft surface, such as a pile of snow. In fact, snow has been known to save lives in the event of a fall from a height.
The amount of force that is absorbed by snow when an object lands on it depends on the density and depth of the snow. For example, fresh powder snow can have a density of around 100 kg/m³, which means that it can absorb more energy than packed snow or ice.
However, even fresh powder snow has its limits. The depth of the snow can also play a role in how much force is absorbed. In the case of Anna and Kristoff’s jump, they would need at least 20 feet of fresh powder snow to land on in order to have a chance of surviving the fall.
Conclusion
So, can you freefall into snow and survive? The answer is: it depends. The height of the fall, the velocity at which you hit the ground, and the depth and density of the snow all play a role in determining whether you will survive the impact of the fall. While snow can certainly help to absorb some of the impact, it is not a guarantee of survival.
So, the answer to Anna and Kristoff’s question is: “Hopefully”.
Freefall Into Snow
Can You Freefall into Snow and Survive?
In the Disney movie Frozen, Anna and Kristoff find themselves in a tricky situation. They have to make a jump from a height of 200 feet, hoping to land safely in a pile of snow. But is surviving such a fall really possible?
Understanding Freefall
Before we answer this question, we need to understand what freefall means. When something is in freefall, it is falling under the force of gravity alone. This means that there is no other force acting upon it, such as lift, drag or air resistance.
Without any air resistance, an object falls at a constant acceleration of 9.8 m/s². This acceleration is known as the acceleration due to gravity or simply, g.
The Physics of a Freefall
The speed at which an object falls depends on how long it has been falling for, and the acceleration due to gravity. We can calculate this using the following formula for freefall:
v = gtHere, v is the final velocity of the object, g is the acceleration due to gravity and t is the time for which the object has been falling.
For example, if a person jumps from a height of 100 feet (about 30 meters), the time it takes them to hit the ground is:
t = sqrt(2h/g)Here, h is the height of the jump. Plugging in the values, we get:
t = sqrt(2 x 30 / 9.8) = 2.44 secondsSo, it takes about 2.44 seconds for a person to hit the ground after jumping from a height of 100 feet.
The Impact of Landing
Now, let’s consider what happens when a person lands on the ground after a jump. The force of the impact of the fall is known as the impact force, which depends on the mass and velocity of the object. The formula for impact force is:
F = maHere, F is the impact force, m is the mass of the object and a is the acceleration due to the impact. In the case of a person landing on the ground after a fall, the acceleration due to impact is the same as the acceleration due to gravity, but in the opposite direction.
Let’s consider a person who weighs 70 kilograms falling from a height of 100 feet (about 30 meters) and hitting the ground. The velocity at which they hit the ground can be calculated as:
v = gt v = 9.8 x 2.44 = 23.91 m/sThe impact force can be calculated as:
F = ma F = 70 x 9.8 = 686 NThis is equivalent to the force that a 70-kilogram object experiences when it is accelerated at a rate of 9.8 m/s². The impact of such a force can be very dangerous, and can easily result in broken bones, internal injuries or even death.
What Happens When You Land on Snow?
The impact force of a fall can be reduced if the falling object lands on a soft surface, such as a pile of snow. In fact, snow has been known to save lives in the event of a fall from a height.
The amount of force that is absorbed by snow when an object lands on it depends on the density and depth of the snow. For example, fresh powder snow can have a density of around 100 kg/m³, which means that it can absorb more energy than packed snow or ice.
However, even fresh powder snow has its limits. The depth of the snow can also play a role in how much force is absorbed. In the case of Anna and Kristoff’s jump, they would need at least 20 feet of fresh powder snow to land on in order to have a chance of surviving the fall.
Conclusion
So, can you freefall into snow and survive? The answer is: it depends. The height of the fall, the velocity at which you hit the ground, and the depth and density of the snow all play a role in determining whether you will survive the impact of the fall. While snow can certainly help to absorb some of the impact, it is not a guarantee of survival.
So, the answer to Anna and Kristoff’s question is: “Hopefully”.