Question

A train and a car having speeds from the same point 72 km/hr and 54 km/hr respectively moving
at right angles to each other. What is the distance between then after 20 seconds?​

Answer 1

Given:

A train and a car having speeds from the same point 72 km/hr and 54 km/hr respectively moving  at right angles to each other

To find:

What is the distance between then after 20 seconds?​

Solution:

Let's assume,

"B" → represents the point where the train and the car starts having their respective speeds

"AB" → represents the distance travelled by train in 20 seconds

"BC" → represents the distance by the car in 20 seconds

"AC" → represents the distance between the train & car after 20 seconds

The speed of the train = 72 km/hr =  $72\times \frac{5}{18} \:m/s = 20 \:m/s$

∴ The distance "AB" travelled by train in 20 seconds is = 20 × 20 = 400 m

The speed of the car = 54 km/hr = $54\times \frac{5}{18} \:m/s = 15 \:m/s$

∴ The distance "BC" travelled by train in 20 seconds is = 15 × 20 = 300 m

Since the train and the car are moving at right angles to each other, so we will apply the Pythagoras theorem to find the distance between them.

∴ The distance "AC" between them after 20 seconds is,

=  $\sqrt{AB^2 + BC^2}$

= $\sqrt{400^2 + 300^2}$

= $\sqrt{250000}$

= $\bold{500}$

Thus, the distance between the train and the car after 20 seconds is → 500 m.

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