If the angular magnification of an astronomical telescope is 43 and the diameter of the objective is 83 mm, what is the minimum diameter of the eyepiece required to collect all the light entering the objective from a distant point source located on the telescope axis?

Explanation:                    

angular magnification (m_θ) = 43                        

diameter of the objective = 83 mm              

                                          = 0.083 m

The minimum diameter of eyepiece                        

Hence, The minimum diameter of the eyepiece required = 1.93 mm

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s