Mechanics 1: Linear Kinematics and Calculus - 3D Math Primer for Graphics and Game Development - page 551

9. A projectile is launched with an initial speed of 150 ft/s, with an angle of
inclination of 40 o from the initial position p 0 = (0 ft, 10 ft).
(a) What is the initial velocity in vector form?
(b) At what time will the projectile reach its apex?
(c) What are the coordinates of the projectile at the apex?
(d) How long will it take the projectile to come back to an altitude of
y = 10?
(e) What will the horizontal displacement be at this time?
10. At the end of our projectile discussion in Section 11.6, we posed the problem
of solving for the time of intersection when the acceleration is an arbitrary
vector a. Take Equation (11.18) and dot both sides with a, and then solve
for t. (Use the quadratic formula, as before.)
11. Complex exponentials such as e ix (were i is the imaginary number such
that i 2 = −1) are very important in differential equations, control systems,
and signal processing. Although it seems odd to put a complex number
into the exponent, Euler's formula gives a meaningful interpretation. To
find this interpretation, you could just go to wikipedia.com and look it up
(which is why the answer is in the back of the topic, anyway). But before
you do, expand the Taylor series of e ix and see whether you can figure it
out for yourself. (Then go online and read about the surprising importance
of this expression.)
12. The International Space Station orbits Earth at approximately 340 km
above Earth's surface. (The orbit is actually elliptical, but ignore that and
assume it moves with uniform circular motion.) Given that the average
speed is about 27,740 km/hr, what is the orbital period? What is the
centripetal acceleration in m/s 2 ? Think carefully!
Of course the mathematicians know how to write all those
numbers. You can read someday in a mathematics book how to
write them all in a high-class and elegant form, but it is first a
good idea to know in a rough way what it is that you are trying
to write about.
— Richard Feynman (1918-1988) from
The Feynman Lectures on Physics