Question
A helicopter is hovering in the air, just above some firefighters who have been surrounded by a fire. A box containing food and additional personal protective equipment for the firefighters is dropped from the helicopter. The helicopter operator uses his instruments to calculate a height of 70 m above the ground. Calculate: If a kind of parachute is placed on the box that reduces the acceleration of the fall by a quarter, calculate again the time it takes the box to fall and the speed with which it hits the ground.
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Answer to a math question A helicopter is hovering in the air, just above some firefighters who have been surrounded by a fire. A box containing food and additional personal protective equipment for the firefighters is dropped from the helicopter. The helicopter operator uses his instruments to calculate a height of 70 m above the ground. Calculate: If a kind of parachute is placed on the box that reduces the acceleration of the fall by a quarter, calculate again the time it takes the box to fall and the speed with which it hits the ground.
Brice
4.8101 Answers
1. La aceleración reducida es:
a' = \frac{g}{4} = \frac{9.8}{4} \, \text{m/s}^2 = 2.45 \, \text{m/s}^2
donde g = 9.8 \, \text{m/s}^2
2. Usar la fórmula de caída libre con aceleración reducida para encontrar el tiempo de caída:
h = \frac{1}{2} a' t^2
donde h = 70 \, \text{m}
3. Sustituir los valores:
70 = \frac{1}{2} \times 2.45 \times t^2
4. Resolver para t
t^2 = \frac{70 \times 2}{2.45}
t^2\approx57.14
t\approx7.56\text{s}
5. Calcular la velocidad con la que impacta el suelo usando:
v = a' \times t
6. Sustituir los valores:
v=2.45\times7.56
v\approx18.52\,\text{m/s}
Por lo tanto, el tiempo en que cae la caja es aproximadamente7.56\,\text{s} 18.52\,\text{m/s}
donde
2. Usar la fórmula de caída libre con aceleración reducida para encontrar el tiempo de caída:
donde
3. Sustituir los valores:
4. Resolver para
5. Calcular la velocidad con la que impacta el suelo usando:
6. Sustituir los valores:
Por lo tanto, el tiempo en que cae la caja es aproximadamente
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