The time the package travels horizontally is equal to the time it takes to hit the ground. This can be calculated using:
s = ut + 1/2 at²; u is 0
480 = 4.9t²
t = 9.90 seconds
Horizontal distance = horizontal speed x time
The speed will be converted to m/s from km/h
= 180 km/hr x 1000m/km x 1hr/3600 seconds x 9.90 seconds
= 495 m
Recall that
<em>v</em>² - <em>u</em>² = 2 <em>a</em> ∆<em>x</em>
where <em>u</em> and <em>v</em> are initial and final velocities, respectively; <em>a</em> is acceleration; and ∆<em>x</em> is the distance traveled (because the skater moves in only one direction).
So we have
(5.8 m/s)² - (8.8 m/s)² = 2 <em>a</em> (6.0 m)
<em>a</em> = ((5.8 m/s)² - (8.8 m/s)²) / (12 m)
<em>a</em> = -3.65 m/s²