Question

Agent Bond is standing on a bridge, 15 m above the road below, and his pursuers are getting too close for comfort. He spots a flatbed truck approaching at which he measures by knowing that the telephone poles the truck is passing are 25 m apart in this region. The roof of the truck is 3.5 m above the road, and Bond quickly calculates how many poles away the truck should be when he drops down from the bridge onto the truck, making his getaway. How many poles is it?

Short answer

The obtained number of poles is 1.5 poles.

Step-by-step solution

Step 1. Calculation of time

The second equation of motion can be used to calculate the time of fall of Agent Bond. To determine the number of poles, divide the distance traveled by the truck with the pole's distance.

Given data.

The height of the bridge is $h=15\mathrm{m}$.

The speed of the truck is $v=25\mathrm{m}/\mathrm{s}$.

The distance of the pole is $d=25\mathrm{m}$.

The roof of the truck above the road is $d_t=3.5\mathrm{m}$.

The relation used to find the displacement is given by.

$\begin{array}{l}y=h-d_t\\ y=15\mathrm{m}-3.5\mathrm{m}\\ y=11.5\mathrm{m}\end{array}$

The relation used to calculate the time of fall is given by.

$y=ut+\frac{1}{2}g{t}^2$

Here, u is the initial velocity whose value is zero.

On plugging the values in the above relation, you get.

$\begin{array}{c}11.5\mathrm{m}=\left(0\right)t+\frac{1}{2}\left(9.81\mathrm{m}/{\mathrm{s}}^2\right)t^2\\ t=1.52\mathrm{s}\end{array}$

Step 2. Calculation of the number of poles

The relation used to calculate the distance covered by the truck is given by.

$D=vt$

Here, u is the initial speed.

On plugging the values in the above relation, you get.

$\begin{array}{l}D=\left(25\mathrm{m}/\mathrm{s}\right)\left(1.52\mathrm{s}\right)\\ D=38\mathrm{m}\end{array}$

To calculate the number of poles, you can use the formula below.

$\begin{array}{c}n=\frac{D}{d}\\ n=\left(\frac{38\mathrm{m}}{25\mathrm{m}}\right)\\ n\approx 1.5\end{array}$

Thus, the number of poles is $n\approx 1.5$.