A 15.0 {\ m g} acorn falls from rest from the top of a 30.0 {\ m m}-high oak tre

Question

A 15.0 { m g} acorn falls from rest from the top of a 30.0 { m m}-high oak tree. When it is halfway to the ground, a 125 { m g} bird gliding horizontally at 80.0 { m cm}/{ m s} scoops it up with its beak.
a) Find the horizontal component of the bird's velocity, just after the bird scoops up the acorn.
b) Find the vertical component of the bird's velocity, just after the bird scoops up the acorn.
c) Find the speed of the bird, just after the bird scoops up the acorn.
d) Find the angle its velocity makes with the vertical, just after the bird scoops up the acorn.

Explanation / Answer

a )the vertical velocity of the acorn is 17.155 m/s conserving momentum the horizontal velocity of the bird is u = 80*125/(125+15) = 71.42 cm/s b) the birds vertical velocity is v= 17.155*15/(125+15) = 1.838 m/s c) the net velocity is V = sqrt (u^2+v^2) = 1.971 m.s d) the angle with the verticle is theta = 21.23 degrees.

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