(a)
The time taken by the cannonball to remain in the air, if it is fired at an angle of
(a)
Answer to Problem 4SP
The time taken by the cannonball to remain in air is
Explanation of Solution
Given info: The vertical component of initial velocity is
Write the equation of motion along the vertical direction.
Here,
When the ball reaches the maximum height the velocity becomes zero. Since in the upward direction the velocity is decreases towards zero, the acceleration due to gravity is negative during the upward motion.
Therefore, Substitute
This is the time taken by the ball to reach the maximum height.
Since total time of flight is twice the time required to reach the high point, the actual time taken by the ball to remain in air is equal to
Conclusion:
Thus, total time taken by the ball to remain in the air is
(b)
The horizontal distance travelled by the cannonball, if it is fired at an angle of
(b)
Answer to Problem 4SP
The horizontal distance travelled by the cannonball is
Explanation of Solution
Given info: The horizontal component of initial velocity is
In the horizontal direction the there is no acceleration, the ball is travelling at constant velocity.
Write the equation of motion along the vertical direction.
Here,
The time taken by the cannonball to remain in air is
Since there is no acceleration in the vertical direction, put
Substitute
Conclusion:
Thus, the horizontal distance travelled by the cannonball is
(c)
The time taken by the cannonball to remain in the air and the horizontal distance travelled by the cannonball, if it is fired at an angle of
(c)
Answer to Problem 4SP
The time taken by the cannonball to remain in air is
Explanation of Solution
If the vertical component of velocity is
Write the equation of motion along the vertical direction.
Here,
When the ball reaches the maximum height the velocity becomes zero. Since in the upward direction the velocity is decreases towards zero, the acceleration due to gravity is negative during the upward motion.
Therefore, Substitute
This is the time taken by the ball to reach the maximum height.
Since total time of flight is twice the time required to reach the high point, the actual time taken by the ball to remain in air is equal to
Write the equation of motion along the vertical direction.
Here,
The time taken by the cannonball to remain in air is
Since there is no acceleration in the vertical direction, put
Substitute
Conclusion:
Thus, time taken by the cannonball to remain in air is
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Chapter 3 Solutions
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