An intercontinental ballistic missile (ICBM) travels at an average speed of 7.03km/sec. The missile contains 459.0Mg of fuel. The fuel is burned at a rate of 313 pounds per second. What would be the maximum distance (in km) the missile could travel until it ran out of fuel? 1Mg=10^6grams
The possible options: A) 2.27*10^4
B)1.04*10^7km C)459km D)1.31*10^4km
E)989km F)4.98*10^4km I got close to F but am unsure
313 pounds * .454 kg/pound = 142 kg
so burns 142 *10^3 grams/second
142*10^3 g/s * t = 459*10^6 g
so
t = (459/142)*10^3 seconds
7.03 km/s * (459/142)*10^3 = distance
= 22.7 *10^3
= 2.27 *10^4 remarkably choice A
To find the maximum distance the missile could travel until it runs out of fuel, we need to calculate the total amount of fuel the missile contains and then divide it by the rate at which the fuel is burned.
First, we need to convert the fuel amount from Mg (megagrams) to grams:
459.0 Mg * 10^6 grams = 459.0 * 10^6 * 10^6 grams = 459 * 10^12 grams
The rate of fuel burn is given as 313 pounds per second. We need to convert pounds to grams:
313 pounds * 453.592 grams/pound = 141,709.896 grams/second
Now we can find the time it takes for the missile to run out of fuel:
Time = Fuel amount / Fuel burn rate
Time = (459 * 10^12 grams) / (141,709.896 grams/second)
Time = (459 * 10^12) / (141,709.896) seconds
Next, we need to find the distance the missile can travel at its average speed of 7.03 km/second:
Distance = Speed * Time
Distance = (7.03 km/second) * (459 * 10^12) / (141,709.896) seconds
Now we calculate the maximum distance:
Distance = (7.03 * 459 * 10^12 / 141,709.896) km
Distance ≈ 22,744 km
Therefore, the maximum distance the missile could travel until it ran out of fuel is approximately 22,744 km.
Comparing this to the options provided, the closest option is A) 2.27*10^4 km, which is equivalent to 22,700 km. So the correct answer is A) 2.27*10^4 km.