In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 65.0 m along a 30° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)(a) starting from restfinal speedm/stime takens (b) starting with an initial speed of 3.00 m/s final speedm/stime taken s

Explanation:

Using equation of motion

v² = u² + 2as  where a = g sinθ, v is final speed and u is initial speed

u = 0 since it is starting from rest

v² = 2 × 65 × 9.8 × sin 30° = √ 637 m²/s² = 25.24 m/s

t, time taken

s = ( v+u)/2 × t

t = 2 s / ( v+ u) =  2× 65 / 25.24 = 5.151 s

b) u = 3.0 m/s

v² = 3² + 2sgsinθ = 9 + (2×65×9.8×sin 30) = 646

v = √646 m²/s²= 25.42 m/s

average velocity = (25.42 m/s + 3 m/s ) / 2 = 14.21 m/s

t = d / average speed = 65 m / 14.21 m/s = 4.574 s

most voltage drop calculators want the distance between the source and destination. then internally, they double it so both the source and return wires are calculated. but you need to know which distance the calculator uses so you're not half of what you should be or double what you should be.

most circuit breakers will not take a #6 directly, so the electrician will have to splice on a smaller pigtail. you also have to upsize the grounding wire when you upsized the ungrounded (hot) wire (see note in 250.122). this will preclude using most cable assemblies, as a cable with #6 copper will most likely only have a #10 grounding conductor. you need a #6 grounding conductor if the circuit is 20a. a #8 cable is no better, as it will have a #10 grounding conductor too. but most 20a breakers will take a #8 directly.

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