Question

A rocket took 300 days to travel 780,000,000 km. It carried 200. tons of propellant (density 0.986 g/mL

a) What is this in miles per hour?

b) Express the fule efficiency in miles per gallon.

Please write out the steps needed to calculate this. Thank you.

Answer 1

We know that 1 Km = 0.62 miles

                     1 day = 24 hours

Given distance travelled, d = 780000000 Km

                                       = 780000000 x 0.62 miles

                                       = 483600000 miles

Time taken , t = 300 days

                    = 300 x24 hour

                    = 7200 hour

Therefore the velocity , v = distance / time

                                    = 483600000 miles / 7200 hour

                                    = 67166.7 miles / hour   ----------(a)

We know that 1 gallon = 3785.41 mL

                      1 ton = 907.2 kg

                   200 ton = 200x907.2 kg

                               = 181440 kg

                               = 181440 x10³ g                      since 1 kg = 10³ g

Given density , d = 0.986 g/mL

So volume , V = mass / density

                     = 181440 x10³ g / 0.986 (g/mL)

                    = 184016227.2 mL

                    = 184016227.2x10^-3 L

                    = 184016227.2x10^-3 x(1/3.78) gallon                     1 gallon = 3.78 L

                    = 48681.5 gallon

483600000 miles distance travelled by 200 tons = 48681.5 gallon

So the efficiency = 483600000 miles / 48681.5 gallon

                         = 9933.95 miles/gallon