Chapter 6.2, Problem 39PPE

To determine

To find: The time of launch of both fireworks A and B after firework B is launched.

Answer to Problem 39PPE

2.5 seconds after Firework B launches both fireworks will explode.

Explanation of Solution

Given information: Two fireworks A and B explode to same heights with speed 220 ft/s and 200 ft/s respectively.

Concept used: As both heights are equation, so first find them in terms of unknown variable time using following formula.

Height $=\text{ Speed}\times \text{time}$

And then both heights are put equal to each other to calculate the unknown variable required time.

Calculation: Let Firework A launches after x seconds. So, Firework B launches before $(x+0.25)$ seconds. Using above formula,

Height covered by A $=220\times xft$

And height covered by B $=200\times (x+0.25)$ft

Now as both cover same heights, so,

  $\begin{array}{l}220x=200(x+0.25)\\ =200x+200\times 0.25\\ =200x+50\end{array}$

Subtract each side $200x$ and then divide by 20,

  $\begin{array}{l}220x-200x=50\\ \Rightarrow 20x=50\\ x=\frac{50}{20}=2.5\end{array}$

Conclusion: 2.5 seconds after Firework B launches, will both fireworks will explode.