kindly solve all parts. Thanks 3. Guiseppe Li keeps having nightmares. He has wo
ID: 2037051 • Letter: K
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kindly solve all parts. Thanks
3. Guiseppe Li keeps having nightmares. He has worked out a system with his step-father, Gerd Hömf, to overcome the fear and get back to sleep. Right after Guiseppe awakes in fright he talks Gerd through his dream. Gerd carefully maps out the dream and then the two of them use calculus to analyze the dream until they both fall asleep from exhaustion. Last night Guiseppe dreamt that he was being chased by creditors across the tundra. Gerd plotted the a- and y-coordinates of Giuseppe's dream body measured in astral meters as a function of dream minutes t r(t) y(t) These are the questions they worked on: (a) The positive y-direction is North. When was Guiseppe running directly North? Directly (b) Guiseppe remembers stopping briefly to empty his pockets which were filled with fortune South? cookies. At what time did this occur? (c) How far did Guiseppe end up from where he began? (d) What was Guiseppe's approximate speed at time t5? (e) What is the (approximate) total distance Giuseppe ran in the first 3 dream minutes?Explanation / Answer
a) slope of x-t curves gives the horizontal component of velocity in x direction. Similarly slope of y-t curve gives the component of velocity in y direction.
Now, if the x component of velocity is zero then particle only has y component which maybe positive ( north) or negative (south) in terms of direction. At t=1 sec slope of x-t curve is zero and that of y-t curve is positive therefore particle is moving in north. Following the same logic, at t=3 sec particle is moving south.
b) at t=7 sec slopes of both curves are zero that is both components of velocity are zero. Hence particle is not moving. That is. It stops
c) at the end of both the curves x coordinate is zero and y coordinate is 3m. Thus guisiseppe is 3m north from initial position.
d) slope of curves at t=5 sec. (Slope)x = 2 (slope) y=1. Thus speed is 2.236 mper seconds
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