Free-Falling Object In Exercises 103 and 104, use the position function s ( t ) = − 4.9 t 2 + 200 , which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t Find the velocity of the object when t = 3 .
Free-Falling Object In Exercises 103 and 104, use the position function s ( t ) = − 4.9 t 2 + 200 , which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t Find the velocity of the object when t = 3 .
Solution Summary: The author explains the formula used to calculate the velocity of an object at t=3 seconds.
Free-Falling Object In Exercises 103 and 104, use the position function
s
(
t
)
=
−
4.9
t
2
+
200
, which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time
t
=
a
A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related
rates questions below. (Hint: Use two carefully labeled similar right triangles.)
(a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt=
feet/sec.
(b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt=
feet/sec.
Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
Step 1
Using the diagram of a right triangle given below, the relation between x, y, and z is
z²
= x²+
+12
x
Step 2
We must find dz/dt. Differentiating both sides and simplifying gives us the following.
2z
dz
dt
dx
2x.
+2y
dt
dx
dy
dz
x
+y
dt
dt
dt
2z
dy
dt
×
dx
(x+y
dt
dy
dt
An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters.
9
ground level
Assume that x is increasing at a rate of 3 meters/sec.
(a) Write as a function of x: 0=
(b) When x=10, the angle is changing at a rate of
rad/sec.
(c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R?
○ Yes
○ No
Chapter 1 Solutions
Bundle: Calculus of a Single Variable, 11th + WebAssign Printed Access Card for Larson/Edwards' Calculus, Multi-Term
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