Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 10.3, Problem 60PS
To determine
To show: theforce acting on an object moving with acceleration acts only in a radial direction and explain the condition where
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If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.
Find the acceleration vector.
r(t) = (cos 3t)i + (2 sin t)j
%3D
O a = (-9 cos 3t)i + (-2 sin t)j
O a = (-3 cos 3t)i + (2 sin t)j
O a = (9 cos 3t)i + (-2 sin t)j
O a = (-9 cos 3t)i + (-4 sin t)j
A seasoned parachutist went for a skydiving trip where he performed freefall before deploying
the parachute. According to Newton's Second Law of Motion, there are two forcës acting on
the body of the parachutist, the forces of gravity (F,) and drag force due to air resistance (Fa)
as shown in Figure 1.
Fa = -cv
ITM EUTM FUTM
* UTM TM
Fg= -mg
x(t)
UTM UT
UTM /IM LTM
UTM UTM TUIM
UTM F UT
GROUND
Figure 1: Force acting on body of free-fall
where x(t) is the position of the parachutist from the ground at given time, t is the time of fall
calculated from the start of jump, m is the parachutist's mass, g is the gravitational acceleration,
v is the velocity of the fall and c is the drag coefficient. The equation for the velocity and the
position is given by the equations below:
EUTM PUT
v(t) =
mg
-et/m – 1)
(Eq. 1.1)
x(t) = x(0) –
Where x(0) = 3200 m, m = 79.8 kg, g = 9.81m/s² and c = 6.6 kg/s. It was established that the
critical position to deploy the parachutes is at 762 m from the ground…
A particle moves so that its position vector at time t is given by
r = e cos ti + e sin tj.
Show that at any time t,
(a) its velocity v is inclined to the vector r at a constant angle 37/4
radians.
(b) its acceleration vector is at right angles to the vector r.
Chapter 10 Solutions
Calculus
Ch. 10.1 - Prob. 1PSCh. 10.1 - Prob. 2PSCh. 10.1 - Prob. 3PSCh. 10.1 - Prob. 4PSCh. 10.1 - Prob. 5PSCh. 10.1 - Prob. 6PSCh. 10.1 - Prob. 7PSCh. 10.1 - Prob. 8PSCh. 10.1 - Prob. 9PSCh. 10.1 - Prob. 10PS
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