Question

4. A bird is flying along the +x-direction at a height 8.0 m above the ground with a constant speed 15 m/s. When the bird passes directly overhead of a shooter, the shooter fires his gun. a) At what angle above the ground should the shooter fire the gun such that the bullet hits the bird? Assume the speed of the bullet is 20 m/s. b) What should be the minimum height for the bird to fly at such that it avoids the bullet? Hint: This is a projectile motion problem.

Answer 1

Trick :: Horizontal component of Velocity of bullet is eqaul to bord velocity.

A)Hence if V is velocity at angle theta.

Then X direction velocity is V cost theta

V cos theta = 15 { given V is 20m/s}

20 cos theta = 15

Theta = 0.72 radian.

B) trick : height of bird should be higher than height of bullet.

Calculating height of bullet that is (V in y direction )² / 2g

Putting values 20 × sin 0.72 / 2 × 9.8 = 8.9 mm

So height of bird must be above then 8.9m or 9m