Answer:
Speeds of 1.83 m/s and 6.83 m/s
Explanation:
Based on the law of conservation of momentum,
where m represents mass, 
is the initial speed before impact, 
and 
are the velocities of the impacted object after the collision and of the originally stationary object after the impact.
Thus, 
After the collision, the kinetic energy doubles, therefore:
Substituting the initial velocity of 5 m/s provides the equation needed to proceed.
We know that leads to 
Using the quadratic formula leads us to solve for the speeds after the explosion, specifically where a=2, b=-10, and c=-25. 
By substituting the values, the solution yields results for the speeds of the blocks, which are ultimately 1.83 m/s and 6.83 m/s.
Answer:
U = 1 / r²
Explanation:
In this problem, the task does not require calculating potential energy via the force equation since these two variables are interconnected.
F = - dU / dr
This derivative represents a gradient, meaning it indicates direction, leading us to write
dU = - F. dr
The formula for force becomes
F = B / r³
Now, let’s apply this in the integral:
∫ dU = - ∫ B / r³ dr
Here, the force aligns with the displacement, simplifying the scalar product to the product of magnitudes.
Now, we can solve the integrals:
U - Uo = -B (- / 2r² + 1 / 2r₀²)
To finalize the calculations, a reference point for energy must be designated; commonly, potential energy is set to zero (Uo = 0) at infinity (r = ∞).
U = B / 2r²
Substituting B = 2, we arrive at:
U = 1 / r²
