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An arrow is shot straight up into the air and on its return strikes the ground at 260 ft/s, imbedding itself 9.0 in. into the ground. Find (a) the acceleration (assumed constant) required to stop the arrow, and (b) the time required for the ground to bring it to rest.

An arrow is shot straight up into the air and on its return strikes the ground at 260 ft/s, imbedding itself 9.0 in. into the ground. Find (a) the acceleration (assumed constant) required to stop the arrow, and (b) the time required for the ground to bring it to rest.

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Given:
Initial speed of the arrow with which it strikes the ground, v0 = 260 ft/s.
Final speed of the arrow, v = 0 ft/s.
Distance travelled by the arrow in ground, x = 9.0 in.
(a) The distance travelled by the arrow is converted from inches to feet as:
232-1569_6.PNG
Therefore the distance travelled by the arrow in ground, before coming to rest is 0.75 ft.
Let us assume that the acceleration on arrow by the action of ground is a.
From the equation of kinematics, we have
232-1984_7.PNG
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:

232-364_8.PNG
232-241_9.PNG
(b)Let us assume that the time taken by the arrow to come at rest is given by t,
Then from the equation of kinematics, we have
v = v0 + at
Substitute the given values and the calculated value of a to get time t as:
232-1942_10.PNG

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