
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Material Type: Exam; Class: Calculus 3 - Advanced; Subject: Mathematics; University: Mesa Community College;
Typology: Exams
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Chapters 12 and 13 - ALL WORK IN YOUR BLUE BOOK! Problems equally weighted
2
. Initially, the object’s position and
a.) Find the object’s position vector function for any time, t.
b.) Find the time of object’s impact (ground is located on the x-y plane).
c.) Find the location of impact, i.e., the impact position vector.
d.) Find the impact velocity vector and the impact speed.
f.) Find the range of the particle in space. (straight-line distance between initial and impact positions)
g.) Find the trajectory path-length of the particle. (total arc length of the object’s flight)
h.) Find the maximum altitude experienced by the object during its flight.
t
t 0
t
t
of intersection of these curves.
3 2
3 2
a.) Velocity and Speed
b.) Acceleration in terms of its base vectors then in terms of its tangential and normal components.
c.) Show that the two forms of acceleration in part b are equivalent.
d.) TNB frame
e.) Curvature and torsion of path
f.) Equations of the osculating, normal, and rectifying planes.
g.) Radius of the osculating circle.
7.) Reduce the following quadric surfaces into standard form, classify the surface, and sketch it. Label your graph.
2
2
2
2
2
2
2
2
8.) Show that the line that passes through the points (1,2,7) and (-2,3,-4) and the line that passes through the points (2,-1,4) and
(5,7,-3) are skew, then find the distance between them.
2
2
2
11.) A baseball is hit 3 feet above the ground at 100 ft/sec and at an angle of π/4 with respect to the ground.
a.) Find the maximum height reached by the baseball.
b.) Will the ball clear a 10-foot-high fence located 300 feet from home plate?
12.) A surface consists of all points P such that the distance from P to the plane y=1 is twice the distance from P to the point
(0,-1,0). Find the equation for this surface and identify it.
increases. Also identify and sketch the surfaces that the curve lies within.
3 2
15.) Find the point at which the line
y z