A cyclist and a motorist ride on roads intersecting at right angles. The speeds of the cyclist and motorist relative

A cyclist and a motorist ride on roads intersecting at right angles. The speeds of the cyclist and motorist relative to the roadside posts are, respectively, 8 m / s and 15 m / s. What is the modulus of speed of a motorist relative to a cyclist?

Given:

v1 = 8 m / s – the speed of the cyclist relative to the road;

v2 = 15 m / s – vehicle speed relative to the road.

It is required to determine v (m / s) – the speed of the car relative to the cyclist.

According to the condition of the problem, the roads along which the car and the cyclist travel intersect at right angles. This means that their speeds are also perpendicular to each other. Then, adding the vectors of the velocities v1 and v2, we obtain:

v = (v1 ^ 2 + v2 ^ 2) ^ 0.5 = (8 ^ 2 + 15 ^ 2) ^ 0.5 = (64 + 225) ^ 0.5 = 289 ^ 0.5 = 17 m / s …

Answer: the speed of the car relative to the cyclist is 17 m / s.