An image of Pacman enters a rectangular video screen at one corner, A, as shown,

Question

An image of Pacman enters a rectangular video screen at one corner, A, as shown, His initial velocity is 50 cm/s directed along the screen diagonal AC. You set the controls so Pacman moves with a constant acceleration A(x) = -16cm/s/s, A (y) = -20 cm/s/s. Show conclusively through which edge of the screen Pacman passes on his way out. B ________________ C
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A D
An image of Pacman enters a rectangular video screen at one corner, A, as shown, His initial velocity is 50 cm/s directed along the screen diagonal AC. You set the controls so Pacman moves with a constant acceleration A(x) = -16cm/s/s, A (y) = -20 cm/s/s. Show conclusively through which edge of the screen Pacman passes on his way out. B ________________ C
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A D

Explanation / Answer

Initial speed u = 50 cos45 i + 50 sin45 j                        = 35.35 i + 35.35 j   cm/s Final speed v = 0 Acceleration a = -16 i - 20 j cm/s^2 = 25.61 cm/s^2 Time t = 50/25.61 = 1.952 s Displacement S = ut + (1/2)at^2                         = (35.35 i + 35.35 j )(1.952) + (0.5)(-16 i - 20 j)(1.952)^2                         = (69 i + 69 j) - (30.48 i + 38.1 j)                         = 38.52 i + 30.89 j Direction ? = Tan^-1[30.89/38.52]                   = 38.7  (below 45 degrees) So we conclude that packman passes out from the edge CD

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