The diagram given below shows a ski jump. A skier weighing 60 kgf stands at A at the top of ski jump. He moves from A and takes off for his jump at B.
a: calculate the change in the gravitational potential energy of the skier between A and B.
b: If 75% of the energy in part (a) becomes kinetic energy at B, calculate the speed at which the arrives at B.
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Answer:
Mass of skier =60kg
loss in potential energy=mg(h1-h2)
60*10*(75-15)
60*10*60=3.6*10to the power 4J
Answered by
10
Given:
Weight of the skier, i.e., mg = 60 kgf
Height of A, h1 = 75 m
Height of B, h2 = 15 m
KE at B = 75% of the change in the gravitational potential energy of the skier between A and B.
To Find:
(a) The change in the gravitational potential energy of the skier between A and B.
(b) The speed of skier at which he arrives at B.
Calculation:
(a) Change in the gravitational potential energy = PE at A - PE at B
⇒ ΔPE = mgh1 - mgh2
⇒ ΔPE = mg (h1 - h2)
⇒ ΔPE = 60 × 9.8 × (75 - 15)
⇒ ΔPE = 588 × 60
⇒ ΔPE = 35280 J = 35.28 kJ
(b) KE at B = 75 % of ΔPE
⇒ 1/2mv² = (75/100) × 35280
⇒ 1/2 × 60 × v² = 26460
⇒ v² = 26460/30
⇒ v² = 882
⇒ v = 29.7 m/s
- So, the change in the gravitational potential energy of the skier between A and B is 35.28 kJ and the speed of skier at which he arrives at B is 29.7 m/s
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