Download Homework 2

Homework 2 (due Friday 2/5)
Your Physics ID number (get from blackboard)____________________
Room and Group Letter (the group you are in for activity time, i.e. if you are in group A in room 301, write 301-A)_____
1. A plane is supposed to fly to a landing strip that is 300 miles away due northeast from it’s starting point (45 degrees
north of east). The pilot screws up though, thinking that he’s supposed to fly due northwest. He doesn’t realize his
mistake until after he has been flying for an hour at a constant 250 mph, relative to the ground. From the moment he
realizes his mistake, assuming the time it takes him to turn the plane is negligible (so assuming he can turn instantly),
how long would he need to fly, and in what direction, to get to the airport? Assume he continues to fly at 250 mph
relative to the ground. (hint: draw a picture!!)
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2. Let’s consider the same situation as the previous problem, but now assume that the 250 mph speed of the plane is
relative to the air, not the ground. The air is constantly moving at a speed of 50 mph at 20° north of east. If the pilot
wants to fly due northwest (since he thinks the airport is in that direction) relative to the ground, then he needs to take
that into account, and fly in a different direction relative to the air. If his plane travels at 250 mph relative to the air,
determine what direction he should fly in (relative to north and west) so that the plane will be traveling due northwest
(45 degrees north of west) relative to the ground.
Note that this is similar to the previous problem, but there is a shift in what is known and what is unknown.
Making the angle of one of the vectors you are adding unknown makes this a much harder problem mathematically.
However, since there are only two vectors, you can do it fairly easily with the law of cosines (update – ok, you can do it
with the law of cosines, but I shouldn’t say it’s fairly easy. You need to first determine geometrically what the angle is
between the wind and the direction he wants to fly, so you know one of the angles of the triangle, and then use the law
of cosines twice). For full credit though, also try doing it with regular vector addition. Doing it that way, focus on the fact
that you know the angle of the final vector (the velocity of the plane relative to ground should be 45 degrees north of
west), which means you can use a trig function to relate the x and y components of the velocity of the plane relative to
ground. You will need to use some math tricks along the way, such as squaring the entire equation at one point, and
using the quadratic formula to solve for either the sin or cos of the unknown angle.
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3. Three dogs are playing tug-of-war with a chew toy. Rocky is pulling due north with a force of 40 pounds. Chester is
pulling 30° south of east with a force of 50 pounds. Pookie Bear, the biggest and meanest of the dogs, is pulling 40° west
of south with a force of 70 pounds. What is the net force on the toy? (give either in vector component form or as
magnitude and direction. Note that you can add force vectors exactly the same as you can add any other vectors – just
break them into components)
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4. Complete this kenken.
48x
2÷
3-
3
3-
1-
8+
4