Question

A bike race against the clock takes place on a straight road. Yan drives at 37 km / h and he starts the course 30s before Christophe. Christophe is traveling at 38.9 km / h.A) How long after Yan's departure will Christophe join him?B) How far from the start will Christophe join Yan?

Answer 1

Given data:

Yan speed;

`u_1=37\text{ km/h}`

Christopher speed;

`u_2=38.9\text{ km/h}`

Christophe starts 30 s later than Yan. Therefore, Christophe takes 30 s less than Yan to reach the same distance.

Part (A)

The distance is given as,

`d=ut`

Let both Yan and Christophe meet at d distance from the start position. Therefore,

`u_1t=u_2(t-30)`

Substituting all known values,

`\begin{gathered} (37\text{ km/h})t=(38.9\text{ km/h})*(t-30) \\ \frac{(37\text{ km/h})}{(38.9\text{ km/h})}=((t-30))/(t) \\ 0.95=1-(30)/(t) \\ (30)/(t)=1-0.95 \\ (30)/(t)=0.05 \\ t=(30)/(0.05) \\ t=600\text{ s} \end{gathered}`

Therefore, 600 s after Yan's departure Christophe will join him.

Part (B)

The distance is given as,

`d=u_1t`

Substituting all known values,

`\begin{gathered} d=(37\text{ km/h})*(600\text{ s}) \\ =(37\text{ km/h})*(600\text{ s})*(\frac{1\text{ hr}}{3600\text{ s}}) \\ \approx6.17\text{ km} \end{gathered}`

Therefore, Christophe joins Yan after 6.17 km from the start.