Explosives are used to blow a rock apart. The explosion blows the rock into three fragments. Two fragments go off at a 76 degree angle to each other--a 6.2 kg piece at 26.7 m/s and a 5.5 kg piece at 23.3 m/s. Calculate the speed of the third piece, if it has a mass of 3.2 kg.
To calculate the speed of the third piece, we can use the principle of conservation of momentum. According to the law of conservation of momentum, the total momentum before the explosion is equal to the total momentum after the explosion.
Let's define the direction of motion of the two fragments as x-axis and y-axis. The momentum of an object is given by the product of its mass and velocity.
Before the explosion:
Momentum of the first fragment = mass of the first fragment * velocity of the first fragment
= 6.2 kg * 26.7 m/s
Momentum of the second fragment = mass of the second fragment * velocity of the second fragment
= 5.5 kg * 23.3 m/s
After the explosion:
The third piece has a mass of 3.2 kg, and its speed (let's call it v) is unknown.
Now, using the principle of conservation of momentum:
Total momentum before the explosion = Total momentum after the explosion
(6.2 kg * 26.7 m/s) + (5.5 kg * 23.3 m/s) = 3.2 kg * v
Simplifying this equation, we can find the value of v, which represents the speed of the third piece.