A canister is dropped from a helicopter 500m above the ground

In summary, the time it takes for the canister to reach the ground depends on the initial velocity and acceleration due to gravity. It will take approximately 3.2 seconds for the canister to reach the ground and it will have a velocity of approximately 31.36m/s when it hits the ground. Air resistance will affect the fall of the canister by decreasing its acceleration, and it will land approximately 500m away from the initial drop point assuming no external forces. Factors such as air resistance, initial velocity, acceleration due to gravity, external forces, mass, shape, and altitude can all affect the fall of the canister.
  • #1
gsphysics
1
0
A canister is dropped from a helicopter 500m above the ground...

A canister is dropped from a helicopter 500m above the ground. Its parachute does not open, but the canister has been designed to withstand an impact velocity of 100m/s. Will it burst or not?

I did the problem, but the back of the book does not agree with me. Where did I go wrong?

s(t)=500-4.9t^2 => s(t)=0 => t=10.1015 secs
I then differentiate to find velocity, which is v(t)=-9.8t, I plug in t from previous => v(10.1015)= -9.8(10.1015)= -99.127m/s. So I said it is able to withstand the impact, but the book says "No." Did I go wrong someplace? Thanks!

*EDIT*
Haha, this is embarrassing, I read the question wrong, I read "Will it burst or not?" as will it survive, so I guess that was the correct method.
 
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  • #2
gsphysics said:
A canister is dropped from a helicopter 500m above the ground...

A canister is dropped from a helicopter 500m above the ground. Its parachute does not open, but the canister has been designed to withstand an impact velocity of 100m/s. Will it burst or not?

I did the problem, but the back of the book does not agree with me. Where did I go wrong?

s(t)=500-4.9t^2 => s(t)=0 => t=10.1015 secs
I then differentiate to find velocity, which is v(t)=-9.8t, I plug in t from previous => v(10.1015)= -9.8(10.1015)= -99.127m/s. So I said it is able to withstand the impact, but the book says "No." Did I go wrong someplace? Thanks!

*EDIT*
Haha, this is embarrassing, I read the question wrong, I read "Will it burst or not?" as will it survive, so I guess that was the correct method.
I read this twice. The question has been answered but with a slight error

I get 98.9947m/s

Its does not burst either way
 
  • #3
Since it is so close, try the calculation with one more decimal place. 9.81 rather than 9.8.
 
  • #4
mathman said:
Since it is so close, try the calculation with one more decimal place. 9.81 rather than 9.8.
I started with the initial conditions and used the OPs approximation but solved without differentiating (it's been a while). I did say it was slight.
 
  • #5
Calculus is completely unnecessary. You have the formulas for distance and velocity.
 
  • #6
mathman said:
Calculus is completely unnecessary. You have the formulas for distance and velocity.
Yes, solved without using it.
 

1. How long does it take for the canister to reach the ground?

The time it takes for the canister to reach the ground depends on the initial velocity of the canister and the acceleration due to gravity. Using the equation d = (1/2)gt^2, where d is the distance, g is the acceleration due to gravity (9.8m/s^2), and t is the time, we can calculate that it will take approximately 3.2 seconds for the canister to reach the ground.

2. What is the velocity of the canister when it hits the ground?

Using the equation v = gt, where v is the velocity and t is the time, we can calculate that the canister will have a velocity of approximately 31.36m/s when it hits the ground.

3. Will air resistance affect the fall of the canister?

Yes, air resistance will affect the fall of the canister. As the canister falls, it will experience air resistance, which will act in the opposite direction of the canister's motion. This will decrease the canister's acceleration and thus affect the time it takes to reach the ground.

4. How far away from the initial drop point will the canister land?

The canister will land approximately 500m away from the initial drop point, assuming that there is no horizontal movement or wind resistance affecting its fall.

5. What factors can affect the fall of the canister?

The factors that can affect the fall of the canister include air resistance, initial velocity, acceleration due to gravity, and any external forces such as wind or horizontal movement. The mass and shape of the canister can also affect its fall, as well as the altitude at which it is dropped.

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