Find the final speed and the time taken for a skier who skies 75 m along a slope that is 15°, measured from horizontal, in the following situations (you may neglect friction). How long (in s) does it take for the skier to reach the bottom of this hill starting from rest?

Final speed = 148.21m.s

Time of flight = 7.82seconds

Explanation:

The motion of the body is a projectile motion.

Projectile is a motion created by an object launched in air and allowed to fall to freely under the influence of gravity.

Taking the maximums height reached H = 75m

Angle of launch = 15°

Using the maximum height formula to get the velocity U of the object

H = U²sin²theta/2g

Where g is the acceleration due to gravity = 9.81m/s²

75 = U²(sin15°)²/2(9.81)

1471.5 = U²(sin15°)²

1471.5 = 0.06699U²

U² = 1471.5/0.06699

U² = 21,965.9

U = √21,965.9

U = 148.21m/s

The time taken for the skier to reach the bottom of this hill starting from rest is the time of flight T.

T = 2Usintheta/g

T = 2(148.21)sin15°/9.81

T = 296.42sin15°/9.81

T = 76.72/9.81

T = 7.82seconds

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