Question

An engine can pull 4 coaches at a maximum speed of 20 m/s. Mass of the engine is twice the mass of every coach. Assuming resistive forces proportional to the weight, approximate maximum speeds of the engine when it pulls 12 and 6 coaches are

• A. 8.5 m/s and 15 m/s respectively
• B. 6.5 m/s and 8 m/s respectively
• C. 8.5 m/s and 13 m/s respectively
• D. 10.5 m/s and 15 m/s respectively

Answer 1

The correct option is A 8.5 m/s and 15 m/s respectively

Let us assume that,

So,

$P=k6mgv\cdots \cdots \left(i\right)$

$P=k14mgv1\cdots \cdots \left(ii\right)$

From the equation $\left(i\right)$ and $\left(ii\right)$ we get,

$6mgv=14mgv1$

$6v=14v1$

$v1=6\times 20/14$

$v1=8.5m/s$

And also,

$6mgv=8mgv2$

$6v=8v2$

$v2=6\times 20/8$

$v2=15m/s$

So,

$v1\&v2=8.5m/sand15m/s$