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

[gsphysics]

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.

 

[pinball1970]

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

 

[mathman]

Since it is so close, try the calculation with one more decimal place. 9.81 rather than 9.8.

 

[pinball1970]

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.

 

[mathman]

Calculus is completely unnecessary. You have the formulas for distance and velocity.

 

[pinball1970]

Calculus is completely unnecessary. You have the formulas for distance and velocity.

Yes, solved without using it.