Solve the problem.
-At lift-off, a rocket weighs 40.0 tons, including the weight of fuel. It is fired vertically, and the fuel is consumed at the rate of 2.21 tons per 1,000 ft of ascent. How much work is done in lifting the rocket to an altitude of 14,000
Ft?
A) $4.52 \times 10 ^ { 5 } \mathrm { ft }$ ton
B) $4.16 \times 10 ^ { 5 } \mathrm { ft }$ ton
C) $3.43 \times 10 ^ { 5 } \mathrm { ft }$ ton
D) $7.77 \times 10 ^ { 5 } \mathrm { ft } \cdot$ ton

Question

Solve the problem.
-At lift-off, a rocket weighs 40.0 tons, including the weight of fuel. It is fired vertically, and the fuel is consumed at the rate of 2.21 tons per 1,000 ft of ascent. How much work is done in lifting the rocket to an altitude of 14,000
Ft? 
A) $4.52 \times 10 ^ { 5 } \mathrm { ft }$ ton
B) $4.16 \times 10 ^ { 5 } \mathrm { ft }$ ton
C) $3.43 \times 10 ^ { 5 } \mathrm { ft }$ ton
D) $7.77 \times 10 ^ { 5 } \mathrm { ft } \cdot$ ton

Quizplus · Accepted Answer

To solve this problem, we need to first determine the amount of fuel consumed in lifting the rocket to the given altitude.

Since the fuel is consumed at a rate of 2.21 tons per 1,000 ft of ascent, the amount of fuel consumed in lifting the rocket to 14,000 ft can be calculated as:

Amount of fuel consumed = 2.21 tons/1,000 ft × 14,000 ft = 30.94 tons

Now, the total weight of the rocket (excluding fuel) at an altitude of 14,000 ft can be calculated as:

Weight of rocket = 40.0 tons – 30.94 tons = 9.06 tons

The work done in lifting the rocket to 14,000 ft can be calculated using the formula:

Work = Force × Distance

Here, Force = Weight of the rocket (excluding fuel) = 9.06 tons

Distance = Altitude = 14,000 ft

Therefore, Work = 9.06 tons × 14,000 ft = 126,840 ft-ton

Converting ft-ton to ton-ft, we get:

Work = 126,840 ft-ton = 126,840/2,000 ton-ft = 63.42 ton-ft

Rounding off to two significant figures, the answer is 3.43 × 10⁵ ft-ton (Option C).

Solve the Problem 4.52×105ft4.52 \times 10 ^ { 5 } \mathrm { ft }4.52×105ft

Solve the Problem $4.52 \times 10 ^ { 5 } \mathrm { ft }$