Question

A train travels at a constant speed of 60 mi/h and crosses over a road as shown in Fig. 2. If the automobile A is traveling at 45 mi/h along the road, determine the magnitude and direction of the velocity of the train relative to the automobile.

Answer 1

As per the question,

speed of train say v$_t$ =60miles/h

speed of Automobile v$_a$ =45miles/h

Let the speed of the train with respect to automobile be v$_{ta}$

Magnitude |v$_{ta}$ |= $\sqrt{60^2+45^2}$

=$\sqrt{3600+2025}$

=$\sqrt{5625}$

=75miles/h

for direction, Let $\theta$ be the direction

tan$\theta=\frac{v_t}{v_a}$

=$\frac{60}{45}$

=1.33

$\theta=tan^{-1}(1.33)$

$\theta=53\degree$ (with respect to automobile)

Hence the magnitude of relative speed of train with respect to automobile

is 75miles/h and 53$\degree$ with automobile respectively