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# p0248 - 2.48 CHAPTER 2 PROBLEM 48 153 2.48 Chapter 2...

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2.48. CHAPTER 2, PROBLEM 48 153 2.48 Chapter 2, Problem 48 Problem: On a peaceful lake, Boat A has velocity V a i . For a Boat A observer, Boat B appears to have a velocity V b j . Boat B launches a missile with relative velocity 1 2 V a i V b j + v k . The unit vectors i and j are parallel to the lake surface, and k points vertically upward. The missile lands on Boat A and displays a banner that says “BOOM.” Determine the original distance between the boats, L ,asa function of V a , v , and the acceleration of gravity, g . Solution: We know that the absolute velocity of Boat A is v a = V a i We are also given the velocity of Boat B relative to Boat A, which is v b/a = V b j Finally, the velocity of the missile relative to Boat B is v m/b = 1 2 V a i V b j + v k Thus, the absolute velocity of Boat B is v b = v a + v b/a = V a i + V b j and the absolute velocity of the missile is v m = v b + v m/b = V a i + V b j 1 2 V a i V b j + v k Therefore, the absolute velocity of the missile is v m = 1 2 V a i + v k Focusing first on the missile, it moves under the influence of gravity. This means the missile experiences acceleration equal to g k . Hence, its position vector, r m ,isg ivenby

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p0248 - 2.48 CHAPTER 2 PROBLEM 48 153 2.48 Chapter 2...

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