Chapter 2, Problem 60GP

To determine

To Find: The number of poles.

Answer to Problem 60GP

2

Explanation of Solution

Given info:

Height, $h=12\text{ m}$

Speed of truck, $u_t=25\text{ m/s}$

Distance between the poles, $d=25\text{ m}$

Height of the bed of the truck, $h_1=1.5\text{ m}$

Acceleration due to gravity, $g=9.8{\text{ m/s}}^2$

Initial speed of the agent bond, $u=0$

Formula used:

Second equation of kinematics:

  $s=ut+\frac{1}{2}a{t}^2$

Where,

  $s=$ Displacement.

  $u=$ Initial speed.

  $t=$ Time taken.

  $a=$ Acceleration.

Calculation:

Distance fall by the agent bond,

  $\begin{array}{c}s=h-h_1\end{array}$

   $\begin{array}{c}=12-1.5\end{array}$

   $\begin{array}{c}=10.5\text{ m}\end{array}$

Let falling time of agent bond be $t$ :

Form kinematics equation:

  $\begin{array}{c}10.5=0\times t+\frac{1}{2}\times 9.8t^2\end{array}$

    $\begin{array}{c}\therefore \\ t=\sqrt{\frac{2\times 10.5}{9.8}}\\ =1.46\text{ s}\end{array}$

Time taken by truck to cross two successive poles:

  $\begin{array}{c}t\text{'}=\frac{d}{u_t}\\ =\frac{25}{25}\\ =1\text{ s}\end{array}$

Since, agent bond takes 1.46 s, therefore truck should be two poles away when he jumps down from bridge onto truck.

Conclusion:

Hence, number of poles are 2.