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1)A Monkey first notices a lion attacking when the lion is 12.5 m away and movin

ID: 2283530 • Letter: 1

Question

1)A Monkey first notices a lion attacking when the lion is 12.5 m away and moving and the monkey at a speed of 5 m/s. The monkey begins to accelerate away from lion at 3m/s^2 and the lion simultaneously begins to accelerate at 2m/s^2. 1. How long does the monkeys escape last? 2. How far has the monkey traveled when the lion catches up with it? Answers: 1: 5 s ; 2: 37.5 m 2) A cat spots a flowerpot that sails first up and then down past an open window. he pot is in view for a total of 0.50 s, and the top-to-bottom height of the window Is 2.00 m. How high above the window top does the flower pot go? Answer: 2.34 m . Calculate A B and find the angle between A and fi using the dot product. Calculate A x B and find the angle between A and B using the cross product. Answer: we did a problem similar to this one in class. Check your notes.

Explanation / Answer

Xm = 12.5 + 1/2 * 3 * t^2      monkey's coordinate at time t
XL = 5 t + 1/2 * 2 * t^2     lions coordinate
.5 t^2 - 5 t + 12.5 = 0     when the X coordinates are equal or
t^2 - 10 t + 25 = 0
(t - 5)^2 = 0    or t = 5
2. Vf = Vi - 1/2 g t^2      going up
Vf^2 = Vi^2 - Vi g t^2 + 1/4 g^2 t^4
Vf^2 - Vi^2 = 1/4 g^2 t^4 - Vi g t^2 = 2 g S = 4 g
Solve for Vi    (speed at bottom of window)
T = Vi / g    time to reach max height (from bottom of window)
H = Vi T - 1/2 g T^2   Height above "bottom of window"
3. A dot B = 12 + 3 - 2 = 13
A = 9 + 1 + 4 = 14   magnitude of A
B = 16 + 9 + 1 = 26    magnitude of B
cos theta = 13 / (14 * 26) = .0357     theta = 88 deg
Similarly A cross B = A B sin theta
For A cross B evaluate the determinant:
i    j    k
3 1   2
4 3 -1   then
cos theta = (magnitude of vector from determinant) / (14 * 26)