Chapter MPS, Problem 10.10MPS

To determine

To Find: The time after which both rockets will be at the same height.

Answer to Problem 10.10MPS

  $t=0.5\sec$

Explanation of Solution

Given:

  $\begin{array}{l}y=-16t^2+150t+5\\ y=-16t^2+160t\end{array}$

Concept Used:

  $\text{Since for both rocket should be at the same height both equation must satisfy the equality}$

Calculation:

  $\begin{array}{l}y=-16t^2+150t+5\\ y=-16t^2+160t\\ \text{⇒}-16t^2+150t+5=-16t^2+160t\\ \text{⇒}5=160t-150t\\ \text{⇒}10t=5\\ \text{⇒}t=\frac{5}{10}\\ \text{⇒}t=0.5\sec \end{array}$

Conclusion:

Thus the time is $t=0.5\sec$ .