Concept explainers
An object is observed to fall from a bridge, striking the water below 2.50 s later, (a) With what velocity did it strike the water? (b) What was its average velocity during the fall? (c) How high is the bridge?
(a)
The velocity with which the object falling from a bridge strikes the surface of the water after
Answer to Problem 17PEB
Solution:
The velocity with which the object strikes water is
Explanation of Solution
Given data:
The time of travel of water from the bridge to the surface of water is
Formula used:
Write the expression for average acceleration.
Here,
Write the expression for the change in velocity.
Here,
Explanation:
Refer to the expressions for average acceleration and change in velocity. Combine both the expressions and write the expression for average acceleration in terms of initial and final velocity.
Consider the motion of the object from the bridge to the surface of the water. The object falls from the bridge and strikes the surface of the water after
Substitute
Further, solve.
Here, since the gravitational acceleration always acts in the downward direction, therefore, the sign of acceleration is negative. Also, the negative value of final velocity denotes the final velocity is in the downward direction.
Conclusion:
The magnitude of final velocity with which the object strikes water is
(b)
The average velocity of the object during its fall.
Answer to Problem 17PEB
Solution:
The object’s average velocity during the fall is
Explanation of Solution
Given data:
The magnitude of initial velocity and final velocity of the object are
Formula used:
Write the expression for the average velocity.
Explanation:
The magnitude of initial velocity and the final velocity of the object during the fall are
Substitute
Here, only magnitude is taken because direction is not necessary to calculate average velocity. The negative value of final velocity denotes its direction but to find the average velocity, only the magnitude of velocity is needed and thus, the negative sign is not taken.
Conclusion:
The average velocity of the object during the fall is
(c)
The height of the bridge from the water surface.
Answer to Problem 17PEB
Solution:
The bridge is at a height of
Explanation of Solution
Given data:
The average velocity of the object during its fall is
Formula used:
Write the expression for the average velocity in terms of distance and time.
Here,
Explanation:
The average velocity during the fall of the object from the bridge to water is
Substitute
Further, solve for
Conclusion:
The height of the bridge is
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