Solving Linear Motion: Bird Catching Fish

[Cantworkit]

[SOLVED] linear motion

Homework Statement

A bird is flying 30 m above a lake when it drops a fish. Another bird at 35 m immediatley dives and catches the fish before it hits the water. What is the initial velocity of the second bird?


2. Homework Equations
h=h0 + v0t - gt^2/2


3. The Attempt at a Solution

At some point the height of the fish and the height of the second bird are equal.
hfish = 30 - gt^2/2.
hbird = 35 + v0t - gt^2/2. I can solve for t, but I don't know how to get v0.

 

[blochwave]

The way the problem is worded I'm assuming the bird catches the fish immediately before it hits the water? (Otherwise it's impossible without more info, at best you can find the minimum necessary initial speed of the bird by doing as follows...)

If so, you can find t by finding how long it takes the fish to hit the water, and assuming the bird grabs it at that instant.

This is also equivalent to setting Hfish and Hbird equal to 0 and solving the equations simultaneously for t and Vo

 

[Moetasim]

I would like to first clarify the variables in this problem. The initial height of the bird dropping the fish (30 m) and the initial height of the catching bird (35 m) are not relevant to finding the initial velocity of the second bird. What we need to focus on is the height of the fish (hfish) and the height of the catching bird (hbird) at the moment when the catching bird reaches the same height as the fish.

Using the equation provided, we can set hfish = hbird and solve for t, which represents the time it takes for the catching bird to reach the same height as the fish. Once we have t, we can use it to find the initial velocity of the catching bird using the equation v0 = (hbird - h0)/t, where h0 is the initial height of the catching bird (35 m).

Therefore, the initial velocity of the second bird can be found by plugging in the values for hbird, h0, and t into the equation v0 = (hbird - h0)/t. This will give us the answer in m/s, which represents the velocity at which the catching bird must have dived in order to catch the fish before it hit the water.

In conclusion, the initial velocity of the second bird can be calculated by setting the heights of the fish and catching bird equal to each other and solving for t, then plugging in the values for hbird, h0, and t into the equation v0 = (hbird - h0)/t. This method can be applied to other similar linear motion problems to find the initial velocity of an object.