The Bio-Mechanical term that defines managing your force while maintaining balance is "Stability"
The average speed of a moving body is given by:
average speed = total distance / total time
average speed = 560 / 25
22.4 meters per second
The skier is traveling at an average velocity of 22.4 meters per second.
I think you're saying that once you start pushing on the cars, you want to be able to stop each one in the same time.
This is sneaky. At first, I thought it must be both 'c' and 'd'. But it's not
kinetic energy, for reasons I'm not ambitious enough to go into.
(And besides, there's no great honor awarded around here for explaining
why any given choice is NOT the answer.)
The answer is momentum.
Momentum is (mass x speed). Change in momentum is (force x time).
No matter the weight (mass) or speed of the car, the one with the greater
momentum is always the one that will require the greater (force x time)
to stop it. If the time is the same for any car, then more momentum
will always require more force.
The gravitational force <em>F</em> between two masses <em>M</em> and <em>m</em> a distance <em>r</em> apart is
<em>F</em> = <em>G M m</em> / <em>r</em> ²
Decrease the distance by a factor of 7 by replacing <em>r</em> with <em>r</em> / 7, and decrease both masses by a factor of 8 by replacing <em>M</em> and <em>m</em> with <em>M</em> / 8 and <em>m</em> / 8, respectively. Then the new force <em>F*</em> is
<em>F*</em> = <em>G </em>(<em>M</em> / 8) (<em>m</em> / 8) / (<em>r</em> / 7)²
<em>F*</em> = (1/64 × <em>G M m</em>) / (1/49 × <em>r</em> ²)
<em>F*</em> = 49/64 × <em>G M m</em> / <em>r</em> ²
In other words, the new force is scaled down by a factor of 49/64 ≈ 0.7656, so the new force has magnitude approx. 76.56 N.
The answer is 9.8, did this last year in AP Science
