Chapter 4, Problem 61RE

To determine

To find: Whether the canister will burst or not.

Answer to Problem 61RE

The canister will not burst.

Explanation of Solution

Given information:

The height is 500 m and the velocity of impact is $100$ .

Calculation:

The velocity is given as,

  $\begin{array}{c}v={\displaystyle \int a\left(t\right)dt}\\ ={\displaystyle \int \left(-9.8\right)dt}\\ =-9.8t+C\end{array}$

The distance is given as,

  $\begin{array}{c}v={\displaystyle \int v\left(t\right)dt}\\ ={\displaystyle \int \left(-9.8t+C\right)dt}\\ =-4.9t^2+Ct+D\end{array}$

Substitute $v\left(0\right)=0$ in above equation.

  $\begin{array}{l}0=-9.8\left(0\right)+C\\ C=0\end{array}$

Substitute $C=0$ and $t=0$ in above equation.

  $\begin{array}{l}500=-4.9\left(0^2\right)+0\left(0\right)+D\\ D=500\end{array}$

Substitute the values in above equation.

  $\begin{array}{l}v\left(t\right)=-9.8t\\ s\left(t\right)=-4.9t^2+500\\ 0=-4.9t^2+500\\ t=10.102\end{array}$

Substitute the value in above equation to get the velocity.

  $\begin{array}{c}v\left(t\right)=-9.8\left(10.102\right)\\ =99\end{array}$

Since, the velocity is less than 100.

Thus, the canister will not burst.