To determine if the Draught will overtake the dragon, we need to compare their speeds. The calculated speed of the Draught is -6.906 m/s, while the dragon is moving at 19.5 m/s. Therefore, the Draught will not overtake the dragon and Fleur will not secure the win.
In order to determine if the Draught will overtake the dragon, we need to compare their speeds. First, let's determine the speed of the Draught on the rough patch of grass:
Force of friction (Ff) = coefficient of friction (μ) * normal force (Fn)
Ff = 0.35 * (0.6 kg * 9.8 m/s²) = 2.058 N
Net force (Fnet) = Fd - Ff
Fnet = (51.6 N/m)(1.2 m) - 2.058 N = 59.52 N - 2.058 N = 57.462 N
Acceleration (a) = Fnet / m
a = 57.462 N / 0.6 kg = 95.77 m/s²
Now, let's calculate the distance the Draught travels on the icy path:
Use the kinematic equation: x = vot + (1/2)at²
17 m = 0 + (1/2)(-1.4 m/s²)(t)²
t = √(34 / 1.4) = √24.2857 ≈ 4.928 s
Finally, let's find the final velocity of the Draught:
v = vo + at
v = 0 + (-1.4 m/s²)(4.928 s) = -6.906 m/s
Since the dragon is moving at a speed of 19.5 m/s and the Draught has a speed of -6.906 m/s, the Draught will not overtake the dragon and Fleur will not secure the win.