Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 2, Problem 106P
To determine
The expression for the position, velocity and acceleration of the object.
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In physics, one important application of the derivative involves the height of a free – falling object, which can be modeled using the position function.
where h is the height of the object in feet, t is the time in seconds, vo is the initial velocity (in feet per second), and ho is the initial height.
Then, substituting the time, results to the following
hmax = (
)+ (1/2)ay(
Substituting ay = -g, results to
hmax = (
)- (1/2)g(
simplifying the expression, yields
hmax =
x sin
b)
The distance traveled by a projectile follows a uniform motion, meaning, velocity is constant from the start point until it reach the ground along the
horizontal axis, so, the range R can be expressed as
R= Vinitial-xt
Substituting the initial velocity on the x-axis results to the following
R = (
)t
But, the time it takes a projectile to travel this distance is just twice of tmax-height, by substitution, we obtain the following:
R =
x 2 x (
Re-arranging and then applying the trigonometric identity
sin(2x) = 2sin(x)cos(x)
we arrive at the expression for the range R as
R =
sin
The data set given in Table 2 is expected to obey a non - linear relation x = 1/2 at? You are asked to plot (x) versus (t) such as to obtain a straight line graph. Choose a good set of scales for the data, make a careful and accurate graph, and analyze the graph to obtain the value of the acceleration, a, from the slope. TABLE 2 t (s) | 0.2 0.4 | 0.6 0.8 1.0 1.2 x (m) 0.03 0.12 0.27 0.51 0.77 1.14
Chapter 2 Solutions
Physics for Scientists and Engineers
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