Question

A 5000 kg open train car is rolling on frictionless rails at 22 m/s when it starts pouring rain. A few minutes later, the car’s speed is 20 m/s. What mass of water has collected in the car?

Answer 1

Answer:

500 kg

Explanation:

It is given that,

The mass of a open train car, M = 5000 kg

Speed of open train car, V = 22 m/s

A few minutes later, the car’s speed is 20 m/s

We need to find the mass of water collected in the car. It is based on the conservation of momentum as follows :

initial momentum = final momentum

Let m is final mass

MV=mv

$m=\dfrac{MV}{v}\\\\m=\dfrac{5000\times 22}{20}\\\\=5500\ kg$

Water collected = After mass of train - before mass of train

= 5500 - 5000

= 500 kg

So, 500 kg of water has collected in the car.

Answer 2

The mass of the  water collected in the car due to the rain is 500 kg.

The given parameters;

• mass of the car, m = 5000 kg
• velocity of the car, u = 22 m/s
• final speed of the car, v = 20 m/s

The mass of water collected in the car is determined by applying the principle of conservation of linear momentum as shown below;

$m_cu_c = v(m_c + m_w)\\\\5000 \times 22 = 20(5000 + m_w)\\\\110,000 = 100,000 + 20m_w\\\\20m_w = 10,000\\\\m_w = \frac{10,000}{20} \\\\m_w = 500 \ kg$

Thus, the mass of the  water collected in the car due to the rain is 500 kg.

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