<commit_before><!--
  Project Lovelace: Problem I1
  Rocket science (intro/calculations, physics)
-->

{% extends "problems/problem.html" %}

{% block required %}
    <p><b>Required math</b>: None.</p>
{% endblock %}

{% block problem_body %}
    <p>
        We'll try to get you familiar with how Project Lovelace problems work by doing some rocket science! A rocket, say the Saturn V, needs to leave a planet, maybe the Earth, with velocity $v$ but it needs to know how much fuel to carry with it. Luckily you can calculate this with the rocket equation $m_\mathrm{fuel} = M \left( e^{v/v_e} - 1\right)$ where $M = 250,000 \mathrm{kg}$ is the mass of the empty rocket and $v_e = 2,550 m/s$ is the exhaust velocity of the rocket. Your program should read in the velocity $v$ as an input and print the mass of fuel needed.
    </p>
{% endblock %}

{% block input_description %}
    <p>
        The velocity the rocket needs to reach in meters per second (m/s).
    </p>
{% endblock %}

{% block input_example %}
    11186.0
{% endblock %}

{% block output_description %}
    <p>
        The mass of fuel needed by the rocket to escape the planet in kilograms (kg).
    </p>
{% endblock %}

{% block output_example %}
    19843016.2    
{% endblock %}<commit_msg>Rocket science: improved description.<commit_after><!--
  Project Lovelace: Problem I1
  Rocket science (intro/calculations, physics)
-->

{% extends "problems/problem.html" %}

{% block required %}
    <p><b>Required math</b>: None.</p>
{% endblock %}

{% block problem_body %}
    <p>
        We'll get you familiar with how Project Lovelace problems work by doing some rocket science! A rocket, say the <a href="https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-was-the-saturn-v-58.html">Saturn V</a>, needs to escape a planet with velocity $v$ but it needs to know how much fuel to carry with it for its escape. You can calculate the amount of fuel needed with the rocket equation $m_\mathrm{fuel} = M \left( e^{v/v_e} - 1\right)$ where $M = 250,000 \mathrm{kg}$ is the mass of the rocket (with no fuel), $v_e = 2,550 \mathrm{m/s}$ is the exhaust velocity of the rocket, and $e = 2.71828...$ is Euler's number. Your program or script should read in the velocity $v$ as an input and print the mass of fuel needed.
    </p>
{% endblock %}

{% block input_description %}
    <p>
        The velocity $v$ the rocket needs to reach (in meters per second [m/s]) to escape the planet.
    </p>
{% endblock %}

{% block input_example %}
    11186.0
{% endblock %}

{% block output_description %}
    <p>
        The mass of fuel $m_\mathrm{fuel}$ needed by the rocket to escape the planet in kilograms (kg).
    </p>
{% endblock %}

{% block output_example %}
    19843016.2
{% endblock %}
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