A 16.0 g acorn falls from rest from the top of a 32.0 m -high oak tree. When it

Question

A 16.0 g acorn falls from rest from the top of a 32.0 m -high oak tree. When it is halfway to the ground, a 125 g bird gliding horizontally at 80.0 cm/sscoops it up with its beak.

Find the speed of the bird, just after the bird scoops up the acorn.

Express your answer in meters per second to three significant figures.

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Part D

Find the angle its velocity makes with the vertical, just after the bird scoops up the acorn.

Express your answer in degrees to three significant figures.

Explanation / Answer

along verticla initial velocity voy = 0

acceleration ay = -g

displacement y = -h = -32 m

vy^2 - voy^2 = 2*ay*y

vy^2 - 0 = 2*9.8*32

vy = 25 m/s

from momentum conservation

initial momentum = final momentum

mcorn*vcorn + mbird*vbird = (mcorn + mbird)*v

16*-25j + (125*80 i) = (16+125)*v

v = 71 i -2.84 j   m/s

speed v = sqrt(7162+2.84^2) = 84.6 m/s

======================

part D

direction = tan^-1(71/2.84) = 87.8

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