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A projectile is fired from the origin with angle of

ISBN: 9781285740621 127

Solution for problem 3 Chapter 13

Calculus | 8th Edition

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Problem 3

A projectile is fired from the origin with angle of elevation and initial speed v0. Assuming that air resistance is negligible and that the only force acting on the projectile is gravity, t, we showed in Example 13.4.5 that the position vector of the projectile is rstd sv0 cos dt i 1 fsv0 sin dt 2 1 2 tt 2 g j We also showed that the maximum horizontal distance of the projectile is achieved when 45 and in this case the range is R v 2 0yt. (a) At what angle should the projectile be fired to achieve maximum height and what is the maximum height? (b) Fix the initial speed v0 and consider the parabola x 2 1 2Ry 2 R2 0, whose graph is shown in the figure at the left. Show that the projectile can hit any target inside or on the boundary of the region bounded by the parabola and the x-axis, and that it cant hit any target outside this region.(c) Suppose that the gun is elevated to an angle of inclination in order to aim at a target that is suspended at a height h directly over a point D units downrange (see the figure below). The target is released at the instant the gun is fired. Show that the projectile always hits the target, regardless of the value v0, provided the projectile does not hit the ground before D. _R 0 R 0 D y x y x

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Notes from 3/22-3/24 Emerging Adulthood  Ages about 18 to mid-late 20s  When an individual doesn’t feel quite like an adolescent, but also not a full-fledged adult o They feel somewhere in between Romantic and Sexual Relationships in Adolescence and Emerging Adulthoods  Romantic Relationship: mutually acknowledged, ongoing interaction o Affection, current, or anticipated sexual behavior o Distinctive intensity (“limerence”)  Intensive, obsessive thoughts  Involuntary  Need for reciprocation  We start dating in adolescence because… o Biological factors (puberty) o Cognitive factors (understanding of romance) o Familial factors (expectations, restrictions) o Societal factors (expectations, restrictions)  Typical Timeline for development o 15- first kiss, first date o 17- first “I love you”, first time having sex o 18- first serious relationship o 21- cohabitation, moving in together o 27- marriage o 13-16: initiation phase o 17-18: affiliation phase o 19-22: intimate phase o 23-27: committed phase  Typical Timeline for the development of gay/lesbian adolescents o 8- first aware that something is different o 10- first same sex attraction o 14- first self-labeling, disclosure to a friend o 15- disclosure to parent, same sex activity o 18- same sex relationship Notes from 3/22-3/24  Why is adolescence dating important o Sexual identity development o Sexual/romantic competence development o Romantic attachment o Positive effects on development  Positive affect, self-esteem, social competence o Negative effects on development  Depression, conflict, mood swings Nonromantic Sexual Relationships “Hookups”  Based on research, hookups are not taking over college campuses o People tend to think their peers are hooking up more than they actually are o About 50% of college students have hooked up at least once in a year o Only 8% of people, when asked, say their last hookup was with someone they were NOT dating  Are hookups bad o It depends on…  The person  Attitude toward hookups  Motivation for the hookup  The relationship  Knowing the partner before the hookup  Comfort during the hookup  Relationship after the hookup  The situation  Consent  Behaviors and safe sex  Alcohol use  Effects from the first time o If the first time was satisfactory, the person is more likely to have satisfaction with future times o If the person felt guilt or unsatisfied, the person is more likely to not be as satisfied in future times Notes from 3/22-3/24 o Girls are more at risk than boys for negative effects  More likely to feel guilty  Report pain during first time, while boys only report not being satisfied  Importance of the first time o Says a lot for consistency  If satisfied first time, more likely to be satisfied rest of times (and vice versa)  If a condom was used, more likely to continue to use condoms for rest of times Young Adulthood Intimacy v. Isolation  Intimacy o The ability to experience an open, supportive, and tender relationship with another person without fear of losing one’s self o The desire to understand the other person o Concern for the other’s well-being o Disclosure of personal feelings o Demonstration of affection o Ability to put aside one’s self at times because the self is secure o Commitment first to own identity, second to other  Isolation o Self-absorption o Unwillingness to compromise o Fear of losing one’s self The key issue here is connecting to another without fear of losing one’s self; you can only do that when identity is achieved  This applies to both friendships and romantic relationships  Friendships o Friendships come BEFORE romantic relationships o Beginning in adolescence, female friendships are “face to face”  Male friendships are “side by side”  Female friendships Notes from 3/22-3/24 o Emphasis on self-disclosure o Emotional revelations o Spend a good deal of time talking together o Feel shut out when friends refuse to self-disclose o Friendships are therapeutic  Male friendships o Males derive less enjoyment from “relationship talk” as they get older  This is mainly because of socialization o Males emphasize cooperation, leadership, competition o Lower levels of self-disclosure than females  Self-disclosure in friendships o Lowest level: male-male o Higher: male-female o Highest: female-female o Females feel lonely if not self-disclosing o Males do not necessarily feel lonely when they’re not o Data from heterosexual males and females  Food for thought o Do male friendships lack intimacy  Maybe not necessarily, but they lack expression o Females tend to want the same type of intimacy in romantic relationships as they have in close friendships o Males do achieve deeper levels of intimacy in romantic relationships than they are used to in their friendships with males o Potential for trouble here…  (Girls being good at intimacy and want it in romance) + (boys not so good at intimacy and not used to it) =  Trouble  Girl needs to bring down her expectations and guy needs to up his intimacy  Identity precedes intimacy o Males are more likely to enter into a committed relationship AFTER career plans are made  To them, this is AFTER their identity is established (career = identity) o The interpersonal (between 2 people) component of identity is more central for women than men Notes from 3/22-3/24 o Clarification of interpersonal relationships often precedes career plans for females o Women are figuring out who they are in the context of relationships (especially romantic) o Woman marry younger (27 v. 29)  Friendships and marriage o In heterosexual marriage, males often name their wives as their best friend o Women most often name another female as their best friend o Men tend to be more satisfied than women with the amount of empathy and companionship in the relationship o Divorce can be more devastating for males because they lose their best friend and their primary source of intimacy o Woman initiate divorce/break-ups more often than men  Identity status and intimacy o Foreclosed: avoid conflict o Diffused: difficulty with commitment, adopt partner’s identity; lack depth o Moratorium: lack of fidelity (more likely to cheat); or a series of monogamous relationships o Achieved: most successful; higher levels of fidelity  Attachment and intimacy o A positive correlation exists between our ability to be intimate as adults and our attachment status in infancy (longitudinal and retrospective data) o Securely attached (55%): feel close to partner; can depend on them; expect partner to be available and attuned o Insecure anxious (20%): (equivalent to ambivalent) not trusting, clingy, experience jealousy, are overly dependent o Insecure avoidant (25%): uncomfortable being emotionally close; feel uncomfortable with emotional expression; find intimacy unpleasant o Those who are insecure can modify/revise expectations when paired with a secure partner  How do we foster intimacy in relationships o Mutual empathy: being attuned to each other’s feelings and thoughts; being open, vulnerable, connected o Mutual authenticity: to feel and know I am being real, genuine, and honest in relationship, and so is my partner Notes from 3/22-3/24  Authenticity requires being in a relationship; you have to be it, express it, communicate it

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ISBN: 9781285740621

Since the solution to 3 from 13 chapter was answered, more than 292 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus, edition: 8. This full solution covers the following key subjects: projectile, target, height, fired, HIT. This expansive textbook survival guide covers 16 chapters, and 250 solutions. The full step-by-step solution to problem: 3 from chapter: 13 was answered by , our top Calculus solution expert on 11/10/17, 05:27PM. Calculus was written by and is associated to the ISBN: 9781285740621. The answer to “A projectile is fired from the origin with angle of elevation and initial speed v0. Assuming that air resistance is negligible and that the only force acting on the projectile is gravity, t, we showed in Example 13.4.5 that the position vector of the projectile is rstd sv0 cos dt i 1 fsv0 sin dt 2 1 2 tt 2 g j We also showed that the maximum horizontal distance of the projectile is achieved when 45 and in this case the range is R v 2 0yt. (a) At what angle should the projectile be fired to achieve maximum height and what is the maximum height? (b) Fix the initial speed v0 and consider the parabola x 2 1 2Ry 2 R2 0, whose graph is shown in the figure at the left. Show that the projectile can hit any target inside or on the boundary of the region bounded by the parabola and the x-axis, and that it cant hit any target outside this region.(c) Suppose that the gun is elevated to an angle of inclination in order to aim at a target that is suspended at a height h directly over a point D units downrange (see the figure below). The target is released at the instant the gun is fired. Show that the projectile always hits the target, regardless of the value v0, provided the projectile does not hit the ground before D. _R 0 R 0 D y x y x” is broken down into a number of easy to follow steps, and 246 words.

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A projectile is fired from the origin with angle of