An airplane with a speed of 102.3 m/s is climbing upward at an angle of 46degree
ID: 2287099 • Letter: A
Question
An airplane with a speed of 102.3 m/s is climbing upward at an angle of 46degrees with respect to the horizontal. When the plane's altitude is 681 m the pilot releases a package. a) what is the maximum height (as measured from the ground) that the package reached before starting falling down? b) how long did it take the package to hit the ground after its release? c) calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the ground. d) relative to the ground, determined the angle of the velocity vector of the package just before the impact. An airplane with a speed of 102.3 m/s is climbing upward at an angle of 46degrees with respect to the horizontal. When the plane's altitude is 681 m the pilot releases a package. a) what is the maximum height (as measured from the ground) that the package reached before starting falling down? b) how long did it take the package to hit the ground after its release? c) calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the ground. d) relative to the ground, determined the angle of the velocity vector of the package just before the impact.Explanation / Answer
vertical component of the velocity = 102.3sin 46 = 73.6 m/s
this will be initial upward velocity of the package
time taken to start moving downwards
v = u - gt
at highest point v = 0
73.6 = 9.8 t
t = 7.5s
also
v^2 = u^2 - 2aS
v = 0
S = u^2 / 2g = 276.375m
total altitude = 681 + 276.375 = 957.4 m
time taken to reach the ground
S = ut + .5gt^2
u = 0 for the downward journey
S = .5 x 9.8 x t^2
t = 14s
total time to reach ground after being released = 14 + 7.5 = 21.5 s
horizontal component = 102.3 cos 46 = 71m/s
horizontal distance travelled = 71 x 21.5 = 1526.5 m
final velocity = v = at
v = 9.8 x 14 = 137.2m/s
direction of final velocity = Vy/Vx = tan-1 (137.2 / 71)
= 62.6 degrees with horizontal
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