Concept explainers
(a)
The vertical component of initial velocity.
(a)
Explanation of Solution
Given:
The time is
The distance is
The distance is
Formula used:
Write the expression for the vertical displacement.
Here,
Substitute
Solve the above equation for
Calculation:
Substitute
Conclusion:
The vertical component of the initial velocity is
(b)
The horizontal component of initial velocity.
(b)
Explanation of Solution
Given:
The time is
The distance is
The distance is
Formula used:
Write the expression for the velocity.
Here,
Calculation:
Substitute
Conclusion:
The horizontal component of initial velocity is
(c)
The maximum height above the launch point.
(c)
Explanation of Solution
Given:
The time is
The distance is
The distance is
Formula used:
Write the expression for the vertical displacement.
Here,
Substitute
Write the expression for the relation of initial and final velocity.
Here,
Substitute
Solve the above equation for
Substitute
Simplify the above equation.
Write the expression for the resultant velocity.
Here,
Write the expression for the angle.
Write the expression for the horizontal displacement of the projectile.
Here,
Substitute
Solve the above equation for
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The maximum height above the launch point is
(d)
The speed and the angle that the velocity makes with the vertical.
(d)
Explanation of Solution
Given:
The time is
The distance is
The distance is
Formula used:
Write the expression for the relation of initial and final velocity.
Here,
Substitute
Calculation:
Substitute
The speed of the projectile at impact is:
Substitute
The angle for impact is:
Substitute
Conclusion:
The speed and the angle that velocity makes with the vertical is
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Chapter 3 Solutions
Physics for Scientists and Engineers
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