Chapter 2, Problem 12P

To determine

Time taken by the car to reach the truck.

Answer to Problem 12P

30.4 seconds are required to reach the truck.

Explanation of Solution

Given info:

Car is 110 m behind the truck and the speed of the car v = is 88 km/h and the speed of the truck is V = 75 km/h.

Formula used:

Speed (v), time (t) and distance (s) is related as $s=vt$ .

Calculation:

Consider the given situation.

  

Consider that t hour time is required to reach the truck.

So, at t hour, distance travelled by the car is $s=vt=88t\text{km}$

At t hour, distance travelled by the truck is $s_1=Vt=75t\text{km}$

The distance between them is

  $\begin{array}{c}{s}_2=110\text{m}\\ =0.\text{11}\text{km}\end{array}$

So, to reach the truck, the car have to travel a distance $(s_1+s_2)$ km, which is equal to s, the distance travelled by the car in time t hour, that is 88t.

So, $(s_1+s_2)=s$

  $75t+0.11=88t$

  $13t=0.11$

  $\begin{array}{c}t=\frac{0.11}{13}\text{h}\\ \text{=}\text{0}\text{.507}\text{min}\\ \text{=30}\text{.4sec}\end{array}$

Conclusion:

Therefore, time required to reach the truck is 30.4 seconds.