Question

Gayle runs at a speed of 3.95 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayle's mass is 45.0 kg, the sled has a mass of 5.40 kg and her brother has a mass of 30.0 kg.

_________. m/s

Answer 1

as there is no friction hence there is no work done by non conservative force, hence we can say that energy is conserved (initial potential energy + initial Kinetic energy = Final Potential energy + final Kinetic energy)

Or say. we can use Work - Energy Theorem

Initial Kinetic energy = Mv²/2 = (0.5)*(45)*(3.95)² = 351.06J

work done by gravity on Gayle : Mgh = (45) *(9.8)*15 = 6615J

Work Done by gravity on sled = m'gh = (5.4)*(9.8)*15 = 793.8J

Work done by gravity on her brother : mgh' = (30)*(9.8)*10 = 2940J

Final kinetic energy is given by (M+m'+m)(v')²/2 = (45+5.4+30)*(0.5)*(v')² = 40.2 * (v')²

Work done by the forces is equal to the change in the kinetic energy:

i.e.

(work done by gravity on Gayle) + (Work Done by gravity on sled) + (Work done by gravity on her brother) = (Final kinetic energy of Gayle and her brother) - (Initial Kinetic energy of Gayle)

6615 + 793.8 + 2940 = 40.2*(v')² - 351.06

40.2*(v')² = 10699.86

(v')² = 266.16

V' = 16.31 m/s