A water jet is releasing water at the rate of 1.5kg/s and at a speed of 1m/s is focused normally on a 2kg block moving with a uniform velocity 2m/s.The jet is focused in opposite to the motion of the block the speed of the block after the jet is focused for 10seconds is
A) 4.5m/s B)9.5m/s C )7.5m/s D)5.5m/s
To determine the speed of the block after the water jet is focused on it for 10 seconds, we can use the principles of conservation of momentum.
Momentum is defined as the product of an object's mass and its velocity. The law of conservation of momentum states that the total momentum of a closed system (where no external forces act on it) remains constant.
In this case, the system consists of the water jet and the block. Initially, the block has a mass of 2 kg and a velocity of 2 m/s. The water jet has a mass flow rate of 1.5 kg/s and a velocity of 1 m/s.
To find the final velocity of the block after the water jet is focused for 10 seconds, we can use the equation:
(mass of block * initial velocity of block) + (mass flow rate of jet * change in velocity of jet) = (mass of block * final velocity of block)
In this equation, the mass flow rate of the jet multiplied by the change in velocity of the jet gives us the change in momentum of the system.
Given:
Mass of block = 2 kg
Initial velocity of block = 2 m/s
Mass flow rate of jet = 1.5 kg/s
Change in velocity of jet = -1 m/s (since the jet is focused in the opposite direction of the block's motion)
Time = 10 seconds
Plugging in the values into the equation, we get:
(2 kg * 2 m/s) + (1.5 kg/s * -1 m/s) = (2 kg * final velocity of block)
Simplifying the equation, we have:
4 kg·m/s - 1.5 kg·m/s = 2 kg * final velocity of block
2.5 kg·m/s = 2 kg * final velocity of block
Dividing both sides of the equation by 2 kg, we find:
1.25 m/s = final velocity of block
Therefore, the final velocity of the block after the water jet is focused for 10 seconds is 1.25 m/s.
None of the provided answer choices (A, B, C, D) match this result, so it's possible there was an error in the question or answer choices provided.