Concept explainers
(a)
The maximum altitude.
(a)
Answer to Problem 65AP
The maximum altitude for this projectile motion is
Explanation of Solution
Draw the below figure for this condition as.
This is the case of projectile motion. Before the engine fails, car has acceleration up to distance from point
Write the expression for vertical acceleration as.
Here,
Write the expression for horizontal acceleration as.
Here,
Write the expression for initial velocity along vertical as.
Here,
Write the expression for initial velocity along horizontal as.
Here,
This projectile motion is divided into three part. Calculate the distances traveled during each phase of the motion.
Case:1
Refer to above figure at point
Write the expression for final velocity along vertical at point
Here,
Write the expression for final velocity along horizontal as.
Here,
Write the expression for vertical displacement as.
Here,
Write the expression for horizontal displacement as.
Here,
Case:2
Refer to the drawn figure, at point
Rearrange equation (V) in terms of time
Write the expression for horizontal distance cover by the engine as.
Write the expression for vertical distance cover by the engine as.
Write the expression for maximum altitude as.
Here,
Case:3
Refer to above figure, at point
Use third equation of motion to calculate the final velocity along verical at point
Write the expression for equation of motion at point
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the maximum altitude for this projectile motion is
(b)
The total time of fight.
(b)
Answer to Problem 65AP
The total time of flight is
Explanation of Solution
The acceleration is under gravity. The final velocity along vertical is downward direction at point
Write the expression for total time of flight as.
Here,
Write the expression for total flight time as.
Here,
Conclusion:
Substitute
Substitute
Substitute
Thus, the total time of flight is
(c)
The horizontal range.
(c)
Answer to Problem 65AP
The net horizontal range is
Explanation of Solution
Refer to above figure, the horizontal range can be calculated by the sum of distance
Write the expression for horizontal distance cover by the engine as.
Here,
Write the expression for horizontal range as.
Here
Conclusion:
Substitute
Substitute
Thus, the net horizontal range is
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Chapter 4 Solutions
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