Parabolic trajectory In Example 7 it was shown that for the parabolic trajectory r ( t ) = 〈 t , t 2 〉, a = 〈0, 2〉 and a = 2 1 + 4 t 2 ( N + 2 t T ) . Show that the second expression for a reduces to the first expression.
Parabolic trajectory In Example 7 it was shown that for the parabolic trajectory r ( t ) = 〈 t , t 2 〉, a = 〈0, 2〉 and a = 2 1 + 4 t 2 ( N + 2 t T ) . Show that the second expression for a reduces to the first expression.
Solution Summary: The author explains how the expression for the acceleration of the trajectory is reduced to a=2sqrt1+4
Parabolic trajectory In Example 7 it was shown that for the parabolic trajectory r(t) = 〈t, t2〉, a = 〈0, 2〉 and
a
=
2
1
+
4
t
2
(
N
+
2
t
T
)
. Show that the second expression for a reduces to the first expression.
A driver is traveling along a straight road when a buffalo runs into the street. This driver has a reaction time of 0.75 seconds. When the driver sees the buffalo he is traveling at 44 ft/s, his car can decelerate at 2 ft/s^2 when the brakes are applied. What is the stopping distance between when the driver first saw the buffalo, to when the car stops.
Topic 2
Evaluate S
x
dx, using u-substitution. Then find the integral using
1-x2
trigonometric substitution. Discuss the results!
Topic 3
Explain what an elementary anti-derivative is. Then consider the following
ex
integrals: fed dx
x
1
Sdx
In x
Joseph Liouville proved that the first integral does not have an elementary anti-
derivative Use this fact to prove that the second integral does not have an
elementary anti-derivative. (hint: use an appropriate u-substitution!)
1. Given the vector field F(x, y, z) = -xi, verify the relation
1
V.F(0,0,0) = lim
0+ volume inside Se
ff F• Nds
SE
where SE is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
Chapter 14 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.