How do you set up and solve this question Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and Junior as they move across the ice after the collision. Give the answer in m/s. Describe the work you did to get the answer.
conserve momentum. That means
m1*v1 + m2*v2 = mv
25*8 + 55*0 = (25+55)v
To solve this question, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity (momentum = mass x velocity).
Before the collision, Junior's momentum is calculated by multiplying his mass (25 kg) by his velocity (8 m/s). The momentum of Junior is therefore 25 kg * 8 m/s = 200 kg m/s.
Since Ben is initially at rest on the slippery ice, his momentum before the collision is zero (as velocity = 0 m/s).
After the collision, Ben and Junior embrace, and they move together as a single system. Let's assume their combined mass is M kg and their final velocity is V m/s.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Thus, we can write the equation:
(25 kg * 8 m/s) + (55 kg * 0 m/s) = M kg * V m/s
Simplifying further:
200 kg m/s = M kg * V m/s
Now, we need to solve for V, the velocity of Ben and Junior as they move across the ice after the collision.
To find the value of M, we need to know the combined mass of Ben and Junior. Assuming that they combine to have a total mass of 80 kg, we can substitute this value into the equation:
200 kg m/s = 80 kg * V m/s
From this equation, we can solve for V:
V = 200 kg m/s / 80 kg = 2.5 m/s
Therefore, the speed of Ben and Junior as they move across the ice after the collision is 2.5 m/s.
In summary, to solve the question, we used the principle of conservation of momentum and set up an equation to equate the total momentum before the collision to the total momentum after the collision. We then solved for the final velocity of Ben and Junior using the given mass and velocity values.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum of a system before collision is equal to the total momentum after the collision.
Let's denote the initial speed of Ben as V₁ and the final speed of Ben and Junior after the collision as V₂.
The momentum before the collision can be calculated as:
Initial momentum of Ben = Mass of Ben × Initial velocity of Ben
= 55 kg × V₁
Initial momentum of Junior = Mass of Junior × Initial velocity of Junior
= 25 kg × 8 m/s
Since Ben and Junior embrace after the collision, they move together with the same velocity. Therefore, the total momentum after the collision is:
Final momentum of Ben and Junior = (Mass of Ben + Mass of Junior) × Final velocity (V₂)
According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:
55 kg × V₁ + 25 kg × 8 m/s = (55 kg + 25 kg) × V₂
Now, we have an equation with one unknown (V₂), and we can solve it using algebra.
Simplifying the equation:
55V₁ + 200 = 80V₂
55V₁ = 80V₂ - 200
V₁ = (80V₂ - 200) / 55
Finally, we need to plug in the values to find the exact speed of Ben and Junior after the collision.