Question

The International Space Station is about 90 meters across and about 380 kilometers away. One night t appears to be the same angular size as Jupiter. Jupiter is 143,000 km in size. Use serxa to figure out how far away Jupiter is in AU Note: 1 AU= 1.5 x 10-km
a) 6.0 x 10 Au
b) 4.0 AU
c) 9.1 x 1010 AU
d) 4.0 x 10 AU

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The distance is $r_2 = 4 \ AU$

Explanation:

From the question we are told that

    The size of Jupiter is  $s_2 = 143,000 \ km$

    The  length of the International Space Station is $r_1 = 380\ km$

    The  size of the International Space Station is  $s_1 = 90 \ m =0.09 \ km$

The angular size where the same one night and this angular size is mathematically represented as

      $\theta = \frac{s}{r}$

Since  $\theta$ is constant

        $\frac{s_1}{r_1} = \frac{s_2}{r_2}$

substituting values

      $\frac{0.09}{380} = \frac{143000}{r_2}$

=>   $r_2 = 6.04 * 10^{9} \ km$

Now we are told to convert to AU and  1 AU  $= 1.5 * 10^8 \ km$

  So

      $r_2 = \frac{6.04 * 10^8}{1.5*10^{8}}$

      $r_2 = 4 \ AU$