Body Fall Kinematics: Find Time & Velocity at Impact

In summary, to find the time it takes for an object to fall from a height of 409.5m under gravity with an initial velocity of zero, use the formula t = sqrt(2*h/g), where t is the time, h is the height, and g is the gravitational acceleration. The velocity at impact with the ground can be found by multiplying 9.8 (the acceleration due to gravity) by the calculated time.
  • #1
scotthands
25
0

Homework Statement


A body falls from a height of 409.5m under gravity. Determine:
(a) The time taken to reach the ground, if the initial velocity is zero
(b) The velocity at impact with ground.

Homework Equations


s= ut
v= u+at
s=ut + 0.5*at^2

The Attempt at a Solution


i tried using the formulas above but couldn't get anywhere, i guess i need to use 9.8 for the acceleration due to gravity too?
 
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  • #2
Assuming air resistance is neglected you can use the constant acceleration equations to determine the answers. Read through this...it should help clarify...

http://www.pha.jhu.edu/~broholm/l3/node6.html#SECTION00020010000000000000
 
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  • #3
i think I've just to use the equations above and mybe this one too: v^2=u^2+2as
 
  • #4
They are the same, just different notation. The link was to help clarify how to approach the problem.

Find the time it takes for the object to hit the ground first (assuming free-fall on earth). The link will help you there.

Then use that time to determine the velocity (part b of the question).
 
  • #6
BTW, don't forget that the problem states that the initial velocity is zero (it will reduce the equation a little).
 
  • #7
damn, i still can't figure it out, it may be the notation that's confusing me but i don't know.
I have the info from the question: The initial velocity is 0, displacement is 409.5m(ithink)
and the acceleration is 9.8.

I just can't seem to use these values to come up with the time.
 
  • #8
If you look at the first link I gave you, you'll see how this is derived (which is the most important part).

t = sqrt(2*h/g)

where,

t = time it takes for the object to reach the ground
h = the height the object is dropped from
g = gravitational accel.
 
  • #9
.5 * 9.8 * t^2 = 409.5

t = squareroot(409.5/(.5*9.8))

9.8 * t = answer for b and t is the answer for a
 
  • #10
xcvxcvvc said:
.5 * 9.8 * t^2 = 409.5

t = squareroot(409.5/(.5*9.8))

9.8 * t = answer for b and t is the answer for a

The point is not to give the answer to the OP, but rather help them find it themselves so they will actually learn something.
 

Related to Body Fall Kinematics: Find Time & Velocity at Impact

1. How do you calculate the time of impact in a body fall?

The time of impact in a body fall can be calculated using the formula t = √(2h/g), where t is the time, h is the height of the fall, and g is the acceleration due to gravity (9.8 m/s²).

2. What factors affect the velocity at impact in a body fall?

The velocity at impact in a body fall is affected by the height of the fall, the mass and shape of the falling object, and air resistance. Other factors such as the surface material and angle of impact may also play a role.

3. How does air resistance affect the kinematics of a body fall?

Air resistance, also known as drag, can significantly affect the kinematics of a body fall. As the falling object accelerates, the force of air resistance increases, eventually reaching a point where it balances the force of gravity and the object falls at a constant speed (known as terminal velocity). This can impact the time and velocity at impact.

4. What is the relationship between time and velocity at impact in a body fall?

The time and velocity at impact in a body fall are inversely related. This means that as the time of impact increases, the velocity decreases, and vice versa. This relationship can be seen in the formula v = gt, where v is the velocity, g is the acceleration due to gravity, and t is the time.

5. How can the kinematics of a body fall be applied in real-world scenarios?

The kinematics of a body fall can be applied in various real-world scenarios, such as analyzing the impact of a fall on the human body, designing safety equipment for extreme sports, and understanding the mechanics of meteorite impacts. It can also be used to calculate the trajectory and impact of falling objects, such as in engineering and construction projects.

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