Answer: option C. 5 × 10² kg m/s
Explanation:
1) Change in momentum = momentum after landing - momentum just when landing
2) Momentum after landing = mass × velocity after landing = mass × 0 = 0
3) Momentum just when landing = mass × velocity when landing
4) Use the conservation of energy law to find the kinetic energy when landing, KE
KInetic energy when landing = potential energy when jumping
KE = PE
PE = mass×gh
g ≈ 10 m/s²; h = 3 m ⇒ PE = mass×10m/s²×3m = 30mass m²/s²
KE = [1/2]mass×v²
⇒ [1/2]mass×v² = 30mass m²/s²
⇒ v² = 60m²/s²
5) Momentum just when landing
P = mass × √60 m/s
P = mass ×√60 m/s = mass × 7.75 m/s
6) To find the momentum you need the mass of the boy.
Assume different masses:
m = 6.45 kg ⇒ P = 6.45 kg × 7.75 m/s ≈ 50 kg m/s
m = 64.5 kg⇒ P = 64.5 kg × 7.75 m/s ≈ 500 kg m/s = 5 × 10² kg m/s
7) Conclusion: being 64.5 kg a reasonalbe mass for a boy, the answer is the option C. 5 × 10² kg m/s
