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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 3 / Problem 7DQ

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Solved: Sketch the six graphs of the x- and y-components

Chapter 3, Problem 7DQ

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QUESTION:

Problem 7DQ

Sketch the six graphs of the x- and y-components of position, velocity, and acceleration versus time for projectile motion with x0 = y0 = 0 and 0 < α0 < 90o.

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QUESTION:

Problem 7DQ

Sketch the six graphs of the x- and y-components of position, velocity, and acceleration versus time for projectile motion with x0 = y0 = 0 and 0 < α0 < 90o.

ANSWER:

Solution 7DQ

Suppose the projectile was launched at an angle $\alpha{}$ . If $\alpha{}$ lies between $0°$ and $90°$ then both x and y component of the initial velocity will be non zero. Let us also consider the total flight time is $T$ and the upward direction is the positive y direction.

Step 1

Acceleration.

As we know that only acceleration that works for projectile motion is the acceleration due to gravity and which acts vertically downwards. Hence if we write the acceleration in component form, we will have

${a}_{x}(t)=0\ m/{s}^{2}$ ….(1)

${a}_{y}(t)=g=9.8\ m/{s}^{2}$ ….(2)

Here we have considered the vertical direction as y axis and horizontal as x axis.

So the graphical representation for ${a}_{x}$ is

And the ${a}_{y}$ vs $t$ graph is shown below

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