Question

A train is running with uniform velocity in the east direction. A car is running on a road parallel to the track with uniform speed. After some time, the road becomes perpendicular to railway track. The car driver notices that initial speed of train with respect to itself was $7\text{m/s}$ and later on it became $13\text{m/s}$. What can be the true speed of the car?

• A. $8\text{m/s}$
• B. $5\text{m/s}$
• C. $13\text{m/s}$
• D. $7\text{m/s}$

Answer 1

The correct option is B $5\text{m/s}$

Case - I
$V_{TC}=7$
$V_T-V_C=7$ ... (i)

Case - II

$\left|V_{TC}\right|=13$
$\sqrt{V_T^2+V_C^2}=13$
$V_T^2+V_C^2=169$
From equation …(i)
$(V_C+7{)}^2+V_C^2=169$
$V_C^2+49+14V_C+V_C^2=169$
$2V_C^2+14V_C=120$
$V_C^2+7V_C-60=0$
$V_C^2+12V_C-5V_C-60=0$
$(V_C+12)(V_C-5)=0$
$V_C=5\text{m/sec}$