State Newton’s second law of motion - Leaving Cert Physics - Question 12 - 2015

As the skier travels down the slope, gravitational potential energy is converted into kinetic energy. Initially, the skier has gravitational potential energy due to her height, which decreases as she descends and increases her kinetic energy as she accelerates.

To find the maximum velocity, we can use the energy conservation principle. The initial gravitational potential energy is equal to the final kinetic energy:

$mgh = \frac{1}{2} mv^2$

Where:

• $m$ = mass of the skier = 71 kg
• $g$ = acceleration due to gravity = 9.8 m/s²
• $h$ = loss of elevation = 90 m

Calculating potential energy: $PE = mgh = 71 \times 9.8 \times 90$ $PE = 62778 \text{ J}$

Setting this equal to the kinetic energy:

$62778 = \frac{1}{2} \times 71 \times v^2$

Solving for $v$:

$v^2 = \frac{62778 \times 2}{71} \approx 1776.88$ $v \approx 42 m/s$

To find the force that the skier exerts on the snow drift, we use the formula:

$F = \frac{mv}{t}$

Where:

• $m$ = mass of the skier = 71 kg
• $v$ = change in velocity, which is $42 ext{ m/s}$ (final velocity is 0 upon coming to stop)
• $t$ = time to stop = 0.8 s

Thus,

$F = \frac{71 \times 42}{0.8} = 3727.5 ext{ N}$

According to Newton's third law, the force that the snow drift exerts on the skier will be equal in magnitude and opposite in direction to the force that the skier exerts. Therefore, the snow drift exerts a force of approximately 3727.5 N in the opposite direction.