题目
The distance between Mercury and Earth changes due to the orbits of the planets. When Mercury is at its closest point to Earth, it is 48 million miles away. When Mercury is at its furthest point from Earth, it is 138 million miles away. For a science project, Ruby calculates the maximum and minimum amount of time it would take to travel from Earth to Mercury in a spacecraft traveling 55 miles per hour. Approximately what are the times, in days?
解析
水星和地球之间的距离因行星的轨道而变化。当水星离地球最近时,距离为4800万英里。当水星离地球最远时,距离为1.38亿英里。为了一个科学项目,鲁比计算乘坐以每小时55英里速度飞行的航天器从地球到水星所需的最长和最短时间。大约各是多少天?
根据公式\(t=\frac{d}{r}\)(其中\(t\)为时间,\(d\)为距离,\(r\)为速度)
- 当距离\(d = 48000000\)英里,速度\(r=55\)英里/小时,时间\(t_{min}=\frac{48000000}{55}\approx872727.27\)小时。
- 当距离\(d = 138000000\)英里,速度\(r = 55\)英里/小时,时间\(t_{max}=\frac{138000000}{55}\approx2509090.91\)小时。
因为一天有\(24\)小时,所以
- \(t_{min}=\frac{872727.27}{24}\approx36363.64\)天,约为\(36364\)天。
- \(t_{max}=\frac{2509090.91}{24}\approx104545.45\)天,约为\(104545\)天。
所以答案是C选项。