To calculate the work done, you need to consider the changes in kinetic energy (Ek) and gravitational potential energy (Ep). It seems like you have correctly identified the formulas for Ek and Ep.
The change in kinetic energy (ΔEk) can be calculated using the formula ΔEk = 0.5 * m * (vf^2 - vi^2), where m is the mass of the sled and rider, vf is the final velocity, and vi is the initial velocity.
In this case, the mass (m) is given as 70 kg, the final velocity (vf) is given as 15.6 m/s, and the initial velocity (vi) is given as 14.30 m/s.
ΔEk = 0.5 * 70 * (15.6^2 - 14.30^2)
= 0.5 * 70 * (243.36 - 204.49)
= 0.5 * 70 * 38.87
= 0.5 * 2710.9
= 1355.45 J
The change in gravitational potential energy (ΔEp) can be calculated using the formula ΔEp = m * g * (hf - hi), where g is the acceleration due to gravity (9.81 m/s^2), hf is the final height above the ground, and hi is the initial height above the ground.
In this case, the mass (m) is given as 70 kg, the initial height (hi) is given as 3 m, and the final height (hf) is 0 m (touching the ground).
ΔEp = 70 * 9.81 * (0 - 3)
= 70 * 9.81 * -3
= -2061.03 J
Note that the negative sign indicates a decrease in gravitational potential energy as the sled moves downhill.
Now, to calculate the total work done (W), you should sum up the changes in kinetic energy and gravitational potential energy:
W = ΔEk + ΔEp
= 1355.45 + (-2061.03)
= -705.58 J
The resulting work done by the snow on the sled is -705.58 J, indicating that work is being done on the sled by the snow.