While watching the clouds pass by, you notice a European swallow flying horizontally at a height h = 22 m above you. When the swallow is directly overhead, it drops an m = 10.9 kg coconut. From your ornithological studies, you know that the air-speed of this particular species of swallow while carrying such a load is v0 = 7.37 m/s. In this problem you may neglect air friction. Refer to the diagram. Assume the origin of the coordinate system there is at your head. (a) Calculate the magnitude of the angular momentum L, in kg ⋅ m2/s, of the coconut as observed by you at the moment it is released directly overhead. (b) Enter an expression for the x component of the position vector rx(t), in meters, of the coconut with respect to you as a function of the free-fall time t, the free-fall acceleration, the other defined quantities. Let t = 0 be the moment that the coconut is released. (c) Enter an expression for the velocity vector v(t), in meters per second, of the coconut as a function of the given information and the free-fall time t. Let t = 0 be the moment that the coconut is released. Express your answer in unit vector notation. (d) Calculate the magnitude of the angular momentum L, in kg ⋅ m2/s, of the coconut as observed by you one second after it is released directly overhead (t = 1 s). (e) Calculate the magnitude of the angular momentum L, in kg ⋅ m2/s,of the coconut as observed by you immediately before it hits the ground.
While watching the clouds pass by, you notice a European swallow flying horizontally at a height h = 22 m above you. When the swallow is directly overhead, it drops an m = 10.9 kg coconut. From your ornithological studies, you know that the air-speed of this particular species of swallow while carrying such a load is v0 = 7.37 m/s. In this problem you may neglect air friction. Refer to the diagram. Assume the origin of the coordinate system there is at your head.
(a) Calculate the magnitude of the
(b) Enter an expression for the x component of the position vector rx(t), in meters, of the coconut with respect to you as a function of the free-fall time t, the free-fall acceleration, the other defined quantities. Let t = 0 be the moment that the coconut is released.
(c) Enter an expression for the velocity vector v(t), in meters per second, of the coconut as a function of the given information and the free-fall time t. Let t = 0 be the moment that the coconut is released. Express your answer in unit vector notation.
(d) Calculate the magnitude of the angular momentum L, in kg ⋅ m2/s, of the coconut as observed by you one second after it is released directly overhead (t = 1 s).
(e) Calculate the magnitude of the angular momentum L, in kg ⋅ m2/s,of the coconut as observed by you immediately before it hits the ground.
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