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3.7: a)<br />

b)<br />

r ˆ ˆ<br />

2<br />

v = αi<br />

− 2βtj<br />

= (2.4 m s)ˆ i −[(2.4 m s ) t]ˆj<br />

r<br />

2 ˆ<br />

2<br />

a = − βj<br />

= ( −2.4 m s ) ˆ. j<br />

r<br />

c) At t = 2.0s<br />

, the velocity is v = ( 2.4 m s)ˆ i − (4.8 m s) ˆj<br />

; the magnitude is<br />

2<br />

2<br />

−4 .8<br />

(2.4 m s) + ( −4.8<br />

m s) = 5.4 m s , and the direction is arctan ( ) = −63°<br />

. The<br />

2. 4<br />

2<br />

acceleration is constant, with magnitude 2 .4 m s in the − y -direction. d) The velocity<br />

vector has a component parallel to the acceleration, so the bird is speeding up. The bird is<br />

turning toward the − y -direction, which would be to the bird’s right (taking the + z -<br />

direction to be vertical).<br />

3.8:

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