Asked by Catherine
An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is traveling horizontally at 40.0 m/s at a height of 100 m above the ground.
a) How far horizontally from the dropping point does the package strike the ground?
b)What are the x and y velocities before it hits the ground?
a) How far horizontally from the dropping point does the package strike the ground?
b)What are the x and y velocities before it hits the ground?
Answers
Answered by
Arman
s = ut + 1/2 at^2.............since the initial velocity down u = 0
100 = 0 + 1/2(9.81)t^2
t = 4.51 sec
again s = ut + 1/2 at^2...........this time horizontally
s = distance = (40)(4.51) + 1/2(0)(4.51)^2................Notice the acceleration = 0
s = 180.61 m away in the direction of flight
this is the same as saying distance = speed x time.
II. Kinetic Energy = 1/2 mv^2
Potential Energy = mgh
(1/2)m(40)^2 + m(9.81)(100) = 1/2 m v^2............................
divide by m
(1/2) (1600) + 981 = 1/2(v^2)
v = 59.6 m/s
This ia according to the law of conservation of Energy.
Another way to do it is Horizontal and vertical velocity:
Horizontal v = 40 m/s...............since a = 0
Vertical v = u + at = 0 + (9.81)(4.51) = 44.23 m/s
Using pythagoras the resulting v = Squaroot ( 44.23^2 + 40^2 ) = 59.6 m/s
Same answer......and it should be, either way would do..
100 = 0 + 1/2(9.81)t^2
t = 4.51 sec
again s = ut + 1/2 at^2...........this time horizontally
s = distance = (40)(4.51) + 1/2(0)(4.51)^2................Notice the acceleration = 0
s = 180.61 m away in the direction of flight
this is the same as saying distance = speed x time.
II. Kinetic Energy = 1/2 mv^2
Potential Energy = mgh
(1/2)m(40)^2 + m(9.81)(100) = 1/2 m v^2............................
divide by m
(1/2) (1600) + 981 = 1/2(v^2)
v = 59.6 m/s
This ia according to the law of conservation of Energy.
Another way to do it is Horizontal and vertical velocity:
Horizontal v = 40 m/s...............since a = 0
Vertical v = u + at = 0 + (9.81)(4.51) = 44.23 m/s
Using pythagoras the resulting v = Squaroot ( 44.23^2 + 40^2 ) = 59.6 m/s
Same answer......and it should be, either way would do..
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