Question #128867

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.

Expert's answer

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

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