It’s a beautiful day in Corvallis. Mrs. Newton decides to go out and walk her do
ID: 1772388 • Letter: I
Question
It’s a beautiful day in Corvallis. Mrs. Newton decides to go out and walk her dog, Brutus, to the park. Once they arrive at the park, Brutus gets really excited and runs to a tree located at 100 m southeast of where Dr. Mrs. Newton is standing. After he gets to the tree, he sees a squirrel in a tree 80 m to the west of where he is standing and decides to run for it. Just before Brutus gets to the second tree, the squirrel notices him and starts to run in the southeast direction. Brutus, who is now determined to get the squirrel, chases after it. After Brutus runs for 20 m, Mrs. Newton feels bad for the squirrel and decides to call Brutus back to her. Brutus, being a good dog that he is, runs straight back to his beloved owner. (a) How much distance does Brutus has to travel in order to meet Dr. Mrs. Newton? (b) In what direction does he travel? (c) If it takes Brutus 30 seconds to get to Dr. Mrs. Newton, what is Brutus’s average velocity?
Explanation / Answer
A) Let north be y, east be x direction,
Position of Brutus = (100 cos 45 degree - 80 +20 cos 45 degree) i - (100 sin 45 degree + 20 sin 45 degree) j
= 4.85 i - 84.85 j
Distance he need to cover = sqrt (4.85^2 +84.85^2)
= 85 m answer
B) direction = arctan (4.85/84.85)
= 3.27 degree West of North
C) average velocity = 85/30 = 2.83 m/s
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