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At a construction site a pipe wrench strikes the ground with a speed of 24.0 m/s. (a) From what height was it inadvertently dropped? (b) For how long was it falling?

At a construction site a pipe wrench strikes the ground with a speed of 24.0 m/s. (a) From what height was it inadvertently dropped? (b) For how long was it falling?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
Given:
Initial speed of pipe,. v0 = 0 m/s.
Final speed of pipe,. v = 24.0 m/s.
Acceleration due to gravity, g = 9.58 m/s2
(a) Let us assume that the pipe falls from height say x. Since the pipe falls under the action of gravity, the acceleration with which pipe falls is equal to the acceleration due to gravity that is g. However this is true only when the effect of air resistance is neglected.
We also assume that the downward direction of vectors are taken to be positive while the upward as negative. Therefore we do not put g as -g.
From the equation of kinematics, we have
232-1744_5.PNG
Where v represents the final speed of the object under consideration, a is its acceleration, v0 the initial speed and the time for which the object is studied.
We can solve for acceleration from the above two equation by eliminating the variable t.
From the second equation, the time t is given as:
232-1996_6.PNG
232-1360_7.PNG
Round off to two significant figures, to have

x = 19 m

The positive value of x indicates that it was measured from starting point, and the vectors pointing downwards are taken as positive.
Therefore the height from the pipe falls is19m.
(b) It is assumed that the downward direction of vectors are taken to be positive while the upward as negative. Therefore we do not put g as -g.
Let us assume that the pipe fell for time t, then the value of t can be calculated from the equation below as:
232-1052_8.PNG
Substitute the given values and the initial condition x0 = 0 to have

232-386_9.PNG
The negative solution to time t is discarded.
Rounding of the value of time t to 2 significant figures
t = 2.0 s
Therefore the time taken by the pipe to fall down is 2.0s.

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