All moving objects have ____________. A. Force B. Distance C. Momentum D. Time
2 answers:
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Answer:
17.34 m/s
Explanation:
Given:
Mass of lion (m₁) = 109 kg
Initial speed of lion (v₁) = 80.0 km/h (Northward direction)
Mass of gazelle (m₂) = 39.0 kg
Initial speed of gazelle (v₂) = 78.5 km/h (Eastward direction)
Final velocity of both lion and gazelle is,
First, let us convert the speeds from km/h to m/s using the conversion factor.
We know that, 1 km/h = 5/18 m/s
Therefore,
Now, the concept of conservation of total momentum is used here as this is a case of perfectly inelastic collision. In inelastic collision, the masses move together with same velocity after collision.
Here, as the lion and gazelle are moving in directions at right angles to each other, the vector sum of their momentums will give the net initial momentum of the system.
So, initial momentum is given as:
Now, we calculate P₁ and P₂.
Therefore, the net initial momentum of the system is given as:
The final momentum of the system is given as:
From the law of conservation of momentum, the final momentum is equal to the initial momentum. So,
Therefore, the final speed of the lion-gazelle system is 17.34 m/s
To solve the problem, we can use Charle's law, which states that for an ideal gas at constant pressure the ratio between absolute temperature T and volume V remains constant:
For a gas transformation, this law can be rewritten as
(1)
where 1 and 2 label the initial and final conditions of the gas.
Before applying the law, we must convert the temperatures in Kelvin:
The initial volume of the gas is
, so if we re-arrange (1) we find the new volume of the gas:
For a gas transformation, this law can be rewritten as
where 1 and 2 label the initial and final conditions of the gas.
Before applying the law, we must convert the temperatures in Kelvin:
The initial volume of the gas is