Question

An asteroid is going to hit the Earth. To calculate its distance it is observed from 2 diametrically opposite points A, B on Earth. The angle subtended at the asteroid by these two directions of observations is $2^o$. Given the diameter of Earth to be about $1.276\times {10}^7$ m. compute the distance of the asteroid.

• A. $3.75\times {10}^{8}m$
• B. $3.85\times {10}^{8}m$
• C. $3.65\times {10}^{8}m$
• D. none of these

Answer 1

Answer: (A)

Given situation can be drawn as

According to the question

Given,

$\theta =2^o=\frac{\pi }{180}\times 2=0.034$ rad

Distance AB = $1.276\times {10}^{7}m$

We know that the distance can be given as

$D=\frac{AB}{\theta }$

Putting values

$D=\frac{1.276\times {10}^7}{0.034}$

After solving

$=3.75\times {10}^{8}m$

Hence the distance of the asteroid is $3.75\times {10}^{8}m$