Holooly Plus Logo
Holooly Plus Logo

Question 2.7.5: A 1000-kg rocket carrying 2000 kg of fuel is motionless in s...

A 1000-kg rocket carrying 2000 kg of fuel is motionless in space. Its engine starts and its exhaust velocity is 0.7 km/sec. What is its speed when all its fuel is consumed?

The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

Here \mathbf{v}_{0}=\mathbf{0}. Then

\begin{aligned}|\mathbf{v}| &=|\mathbf{u}| \ln \frac{m_{0}}{m}=0.7 \ln \frac{3000}{1000}=0.7 \ln 3 \approx 0.769 \mathrm{~km} / \mathrm{sec} \\& \approx 2769 \mathrm{~km} / \mathrm{hr}(\approx 1720 \mathrm{mi} / \mathrm{hr}) .\end{aligned}

Related Answered Questions

Let f(t) = (cos t)i + (sin t)j . Calculate the following: (a) ∫f(t) dt (b) f,∫0^π/2f(t ) dt

Verified Answer:
(a) \begin{aligned}\int \mathbf{f}(t) d t &...

Let the car of Example 5 have the coefficient of friction µ,. That is, the maximum frictional force that can be exerted by the car on the road surface is µ,mg, where mg is the normal force of the car on the road (the force of the car on the road due to gravity). What is the minimum value µ, can

Verified Answer:
We must have \mu m g \geq 52,083 \frac{1}{3...

A 1500-kg race car is driven at a speed of 150 km/hr on a circular race track of radius 50 m. What frictional force must be exerted by the tires on the road surface to keep the car from skidding?

Verified Answer:
The frictional force exerted by the tires must be ...

Calculate the curvature and radius of curvature of the curve y = 3/x at the point (1, 3).

Verified Answer:
Here d y / d x=-3 / x^{2}, d^{2} y / d x^{2...

Find the curvature and radius ofcurvature of the curve given parametrically by x = (t^3/3) – t and y = t^2 (see Example 2.4.4) at t = 2√2.

Verified Answer:
We have d x / d t=t^{2}-1, d^{2} x / d t^{2...

Show that for a straight line κ(t) = 0.

Verified Answer:
A line can be represented parametrically [see equa...

We certainly expect that the curvature of a circle is constant and that its radius of curvature is its radius. Show that this is true.

Verified Answer:
The circle of radius r centered at ...

An object of mass m moves in the elliptical orbit given by f(t) = a(cos αt)i + b(sin αt)j. Find the force acting on the object at any time t.

Verified Answer:
We easily find that \mathbf{a}(t)=\mathbf{f...

The cannonball of Example 2 has a mass of 8 kg. Find the force acting on the ball at any time t.

Verified Answer:
Here m is constant, so that F = ma = (8kg)(-gj) = ...

A cannon whose muzzle is tilted upward at an angle of 30° shoots a ball at an initial velocity of 600 m/sec.(a) Find the position vector at all times t >= 0.(b) How much time does the ball spend in the air?(c) How far does the cannonball travel? (d) How high does the ball get? (e) How far from the

Verified Answer:
(a) From Example 2.1.6 we find, resolving the init...