(a)
The time taken for the stone to reach the base of the gorge.
(a)
Answer to Problem 69P
The time taken for the stone to reach the base of the gorge is
Explanation of Solution
Write the equation for the time taken for the stone to reach the base of the gorge.
Here,
Conclusion:
Substitute
Thus, the time taken for the stone to reach the base of the gorge is
(b)
The time taken for the stone to reach the ground if it is thrown straight down.
(b)
Answer to Problem 69P
The time taken for the stone to reach the ground if it is thrown straight down is
Explanation of Solution
Write the equation for the vertical distance.
Here,
Conclusion:
Substitute
The value of t can be found by solving the above quadratic equation.
Substitute
As the time must be positive, the time taken for the stone to reach the ground if it is thrown straight down is
(c)
The distance below the bridge the stone will hit the ground.
(c)
Answer to Problem 69P
The distance below the bridge the stone will hit the ground is
Explanation of Solution
Sketch the figure showing the components of velocities.
Figure 1
Write the equation for the vertical distance.
Here,
Write the equation for the horizontal distance.
Conclusion:
Substitute
Find the value of
Substitute
As the time must be positive, the time taken is
Substitute
Therefore, the distance below the bridge the stone will hit the ground is
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