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49. The speed of the boat is constant, given by
v
b
=
d/t
. Here,
d
is the distance of the boat from the bridge
when the key is dropped (12 m) and
t
is the time the key takes in falling. To calculate
t
, we put the
origin of the coordinate system at the point where the key is dropped and take the
y
axis to be positive
in the
downward
direction. Taking the time to be zero at the instant the key is dropped, we compute

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**Unformatted text preview: **the time t when y = 45 m. Since the initial velocity of the key is zero, the coordinate of the key is given by y = 1 2 gt 2 . Thus t = r 2 y g = s 2(45 m) 9 . 8 m / s 2 = 3 . 03 s . Therefore, the speed of the boat is v b = 12 m 3 . 03 s = 4 . 0 m / s ....

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