# Finding time and speed at which skydiver hits the ground

• andrey21
In summary, the conversation discusses the time and speed at which a skydiver would hit the ground if their initial vertical velocity is zero. It is assumed that the acceleration due to gravity is 10m/s^2 and the skydiver is initially 4000m above the ground. Using the equations y' = -gt + A and y = -(1/2)g.t^2 +At +B, it is calculated that the skydiver would hit the ground after 28.284 seconds with a velocity of 282.84 m/s. However, the group also discusses the effects of air friction and the possibility of the parachute failing to open, which would significantly change the speed at which the skydiver hits

#### andrey21

If initial vetical velocity is zero, at what time and how fast does a skydiver hit the ground? Assume that g=10m.s^-2

Given that:
y' = -gt + A y' is the vertical velocity
y = -(1/2).g.t^2 +At +B y is the distance above the ground

In order to solve how long takes skydiver to hit ground I did the following:

0 = -(1/2).g.t^2 +(0)t + 4000
4000 = -(1/2).g.t^2
8000 = g.t^2
800 = t^2
t = 28.284 seconds!

Now from here I am unsure how to find the speed at which hits the ground. Help needed sorry for bad formatting!

Okay so if initial velocity is zero I get:

v = 0 +10.28.284
v = 282.84 m.s^-2
Is this correct?

It seems bit excessive as 282.84m.s^-2 is 632.319 MPH. DOes that seem correct to you?

I must also say the skydivers parachute fails to open so a higher speed on descent would be expected.

Anymore ideas please, help desperatley needed!

Looks ok to me if the initial height is 4000m. 282m/s IS fast, but you've completely neglected air friction. That would slow the skydiver down a lot, even if the chute didn't open.

Ah yes thanks for the post :)

## 1. What factors affect the time and speed at which a skydiver hits the ground?

The main factors that affect the time and speed of a skydiver hitting the ground are the skydiver's mass, air resistance, and the height from which they are jumping.

## 2. How does air resistance affect the descent of a skydiver?

Air resistance, also known as drag, is a force that acts in the opposite direction of motion and increases as the speed of the skydiver increases. This means that the higher the air resistance, the slower the descent of the skydiver.

## 3. Is the time it takes for a skydiver to hit the ground affected by their weight?

Yes, the time it takes for a skydiver to hit the ground is affected by their weight. Heavier skydivers will typically fall faster and hit the ground sooner than lighter skydivers, assuming all other factors are constant.

## 4. What is the equation for calculating the time and speed of a skydiver's descent?

The equation for calculating the time and speed of a skydiver's descent is: t = √(2h/g) where t is the time, h is the height, and g is the acceleration due to gravity (9.8m/s²). The speed can be calculated using the formula v = gt, where v is the final velocity (speed) and t is the time.

## 5. How can a skydiver control their speed during descent?

A skydiver can control their speed during descent by changing their body position. To increase speed, they can streamline their body and decrease air resistance. To decrease speed, they can spread out their limbs and increase air resistance. They can also use a parachute to slow their descent even further.