Suppose while sitting in a parked car, you notice a jogger approaching towards you in the side view mirror of R= 2m. If the jogger is running at a speed of 5ms-1 , how fast the image of the jogger appear to move when the jogger is 39m away?
Open in App
Here, R = 2 m, f = R/2 =2/2 = 1m Using mirror formula, we have
1/v +1 /u = 1/f ====> 1/v = 1/f -1/u
====> 1/v = u-f/fu ===> fu/u-f -----(i)
When jogger is 39 m away, then u = -39m Using Eq. (i), we get
v = fu/u-f = 1(-39) /-39-1 or v = 39/40 m As the Jogger is running at a constant speed 5 m/s, after 1 s, the position of the image for u = -39 +5 ===> -34 m Again using Eq. (i), we get
v = 1-(-34) / -34-1 ===> v = 34/35 m Difference in apparent position of Jogger in 1 s = 39/40-34/35 = 1365-1360/1400 = 1/280 m Average speed of Jogger’s image = 1/280 m/s