(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A bird is flying horizontally at a constant velocity of 2 m/s. 10 meters under the bird, there is a man that wants to shoot the bird. He is holding his gun at an angle of 45 degrees from horizontal. The initial velocity of the bullet is 25 m/s. When the man must open fire?

2. Relevant equations

x = x.init + x.velocity.init * time + 0.5 * accel.x * time^2

y = y.init + y.velocity.init * time + 0.5 * accel.y * time^2

time=t

3. The attempt at a solution

First, I find the x and y components of the initial velocity of the bullet:

x.velocity.init.bullet = 25 * cos(45 degrees) = 17.68 m/s

y.velocity.init.bullet = 25* sin(45 degrees) = 17.68 m/s

Then, since the bird always stays at a height of 10 meters, I find how much time the bullet takes to reach this height.

y = y.init + y.velocity.init * time + 0.5 * accel.y * time^2

10 = 0 + 17.68*t + 0.5*-9.8*t^2

t = 0.702 s

I find the horizontal position of the bullet after 0.702 seconds

x = 17.68m/s * 0.702 s

x = 12.41 m

Now, I find how much time the bird takes to fly 12.41 meters

x = initial x + x.velocity.bird * time

12.41 = 0 + 2*t

t = 6.205 s

The final answer is 6.205-0.702 = 5.503 seconds

Is my work correct?

Sorry for my bad english.

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