A canister is dropped from a helicopter hovering 500m above the ground. Unfortuantly its parachute does not deploy. It has been designed to withstand an impact velocity of 100m/s. Will it burst or not?
Not sure what to do.
Check if $\displaystyle mgh\leq\frac{mv^2}{2}$ where $\displaystyle mgh$ is the potential energy at the drop point and with the ground as zero. Assuming my understanding of impact velocity in this question is correct.
Just plug in the values of the variables into the inequality and see if it holds.
$\displaystyle h=500$ (height)
$\displaystyle v=100$ (velocity)
$\displaystyle g=9.8$ (standard gravity)
$\displaystyle m > 0$ so you can just divide it out.
$\displaystyle 9.8 \cdot 500 \leq 10 \cdot 500$ so it will not burst.
This is not exactly an answer to a calculus question, so I don't think I have interpreted the impact velocity correctly.