Question

men are running along a road at 15km/hr behind one another at equal intervals of 20m. cyclists are riding in the same direction at equal intervals of 30m at what speed in km/hr an observer travelling along the road in opposite direction so that whenever he meets a runner he also meets a cyclist

Answer 1

Answer on Question #44203-Physics-Mechanics-Kinematics-Dynamics

Men are running along a road at $15\mathrm{km/hr}$ behind one another at equal intervals of $20\mathrm{m}$. Cyclists are riding in the same direction at equal intervals of $30\mathrm{m}$ at what speed in $\mathrm{km/hr}$ an observer travelling along the road in opposite direction so that whenever he meets a runner he also meets a cyclist.

Solution

Suppose runner and cyclist reach at same position in time $t$, and the observer has travelled $x$ distance in this time.

Speed of runner is $15\frac{km}{h} = \frac{25}{6}\frac{m}{s}$.

Speed of cyclist is $25\frac{km}{h} = \frac{125}{18}\frac{m}{s}$.

Time $t$ is $\frac{\text{distance travelled}}{\text{speed}}$:

$$t = \frac{20 - x}{\frac{25}{6}} = \frac{30 - x}{\frac{125}{18}} \rightarrow x = 5\mathrm{m}.$$

Putting it in equation we get

$$t = \frac{18}{5}s = 3.6s$$

Speed of observer to travel 5 meter distance in 3.6 sec is

$$v = \frac{5\mathrm{m}}{\frac{18}{5}s} = \frac{25\mathrm{m}}{18s} = 5\frac{\mathrm{km}}{\mathrm{h}}.$$

Answer: $5\frac{km}{h}$.

https://www.AssignmentExpert.com