Answer
See the detailed answer below.
Work Step by Step
The given formula seems to be a conservation of energy equation.
The first term is kinetic energy while the second term seems to be thermal energy done by a friction force that has a coefficient of friction of 0.15 while the object is moving on a tilted surface at $40^\circ$. The last term is the initial gravitational energy.
a) A box of mass 20 kg was initially at rest on a rough surface that has a coefficient of friction between it and the box of 0.15. This surface is tilted about 40$^\circ$ above the horizontal. It was initially at a height of 2.5 m and starts to slide down the incline from rest. Find its speed at the bottom of the tilted surface.
b) See the figure below.
c) Solving the given formula for $v_1$:
We can see that the mass of the box is a common factor, so we can divide both sides by $ 2.5\;\rm kg$. We also need to multiply both sides by 2.
$$v_1=\sqrt{\left[2\times9.8\times 2.5\right]-\left[ 2\times 0.15 \times 9.8\times 2.5\times \dfrac{\cos40^\circ}{\sin40^\circ}\right]}$$
$$v_1=\color{red}{\bf 6.3}\;\rm m/s$$
