A fish is rising vertically to surface of a lake at rate of 2 m/s observes a bird diving vertically towards water at 4 m/s. The refractive index of water is 4/3. what is actual velocity of bird
4.5 m/s
To find the actual velocity of the bird, we need to consider the concept of apparent velocity due to refraction.
Apparent velocity is the velocity of an object observed through a denser medium. In this case, the bird is observed through the water, which has a higher refractive index than air, causing the bird's velocity to appear different.
To calculate the apparent velocity of the bird, we can use the formula:
Apparent Velocity = Actual Velocity / Refractive Index
Given:
Rate at which the fish is rising to the surface = 2 m/s (upwards)
Rate at which the bird is diving towards the water = 4 m/s (downwards)
Refractive index of water = 4/3
Let's calculate the apparent velocity of the bird:
Apparent Velocity of the bird = -4 m/s / (4/3)
= -4 m/s * (3/4)
= -3 m/s
Since the apparent velocity is negative (-3 m/s), it indicates that the bird is diving downwards.
Hence, the actual velocity of the bird is 3 m/s downwards.