A hunter fires 50 g bullets from a machine gun. If each bullet moves with a velocity of 150ms−1 how many such bullets are to be fired into a tiger of mass 60 kg coming towards him with a velocity of 10ms−1 in order to stop the tiger?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullets are fired is equal to the total momentum after the bullets hit the tiger.
The momentum of an object is calculated by multiplying its mass by its velocity (P = mv).
Let's first calculate the momentum of the tiger before the bullets hit:
Momentum of the tiger = mass of the tiger × velocity of the tiger
= 60 kg × 10 m/s
= 600 kg⋅m/s
Now, let's calculate the momentum of each bullet:
Momentum of each bullet = mass of each bullet × velocity of each bullet
= 0.05 kg × 150 m/s
= 7.5 kg⋅m/s
To stop the tiger, the total momentum of all the bullets should be equal to the momentum of the tiger.
Number of bullets = Total momentum of the tiger / Momentum of each bullet
= 600 kg⋅m/s / 7.5 kg⋅m/s
= 80 bullets
Therefore, in order to stop the tiger, the hunter needs to fire 80 bullets.