A truck is descending a winding mountain road. When the truck is 1480 m above sea level and traveling 15 m/s, its brakes fail. What is the maximum possible speed of the truck at the foot of the mountain 550 m above sea level

The maximum possible speed of the truck at the foot of the mountain at 550 m above sea level is 135.91

Explanation:

Mechanical energy is the ability of a body to generate motion and perform mechanical work.

In other words, mechanical energy is that related to both the position and the movement of bodies.

Mechanical energy is calculated by:

Em = Ep + Ec

where Em is the mechanical energy (J), Ep the potential energy (J) and Ec the kinetic energy (J).

The mechanical energy of a body remains constant when all the forces acting on it are conservative.

Potential energy refers to the position of a mass in space and is calculated by:

Ep = m • g • h

where m is the mass (kg), g the gravity of the Earth (9.81 ) and h is the height (m)

Kinetic energy is the energy that an object has due to its movement and its expression for the calculation is:

Ec = ½ m • v²

Where m is the mass (Kg) and v the speed (m/s).

The truck would have  the maximum possible speed if friction were ignored. Then:

So the forces are conservative and the mechanical energy is constant. So:

Em initial= Em  final

So:

Ep initial + Ec initial= Ep final + Ec final

m • g • h  initial + ½ m • (v initial)² = m • g • h  final + ½ m • (v final)²  [mass and gravity remain constant]

As the mass m is found in all terms, they can be simplified and it is obtained:

g • h  initial + ½ • (v initial)² = g • h  final + ½ • (v final)²  

Taking as a reference the zero of the potential energy at sea level and isolating the value of vf, you obtain the expression:

Being:

and replacing:

you get:

v final= 135.91

The maximum possible speed of the truck at the foot of the mountain at 550 m above sea level is 135.91