A motor ship with a length of l = 300 m moves along the lake at a certain speed. The boat with a speed

| June 26, 2021 | education

A motor ship with a length of l = 300 m moves along the lake at a certain speed. The boat with a speed, the modulus of which is V1 = 90.0 km / h, passes from the stern to the bow of the moving motor ship and back in time t = 35.7 s. The speed module of the ship is?

To find the speed module of the motor ship, we will use the formula: t = Lt / (Vk + Vt) + Lt / (Vk – Vt) = (Lt * (Vk – Vt) + Lt * (Vk + Vt)) / ((Vk + Vt) ) * (Vk – Vt)) = Lt * (Vk – Vt + Vk + Vt) / (Vk2 – Vt2) = Lt * 2Vk / (Vk2 – Vt2).

Values of variables: t – duration of boat movement (t = 35.7 s); Lt is the length of the ship (Lt = 300 m); Vк – the module of the boat speed (Vк = 90 km / h = 25 m / s).

Let’s substitute the variables and find the speed module of the motor ship:

37.5 = 300 * 2 * 25 / (25 ^ 2 – Vt ^ 2).

37.5 * (25 ^^ 2 – Vt2) = 15000.

23437.5 – 37.5Vt ^ 2 = 15000.

Vt = √ ((23437.5 – 15000) / 37.5) = 15 m / s.

Answer: The speed module of the motor ship is 15 m / s.



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