part1. A colony of troglodytes has been in a lengthy feud with its neighbors on
ID: 2176160 • Letter: P
Question
part1. A colony of troglodytes has been in a lengthy feud with its neighbors on the adjacent cliff. Colony A finally develops an important mili- tary breakthrough: it rolls bombs off its cliff at known rates of speed, thus gaining pinpoint accuracy in its attacks. If the cliffs are separated by 46 m and a bomb is rolled at 5.2 m/s, how far down the opposite cliff will it land? The acceleration due to gravity is 9.8 m/s2 .Answer in units of m
part2. The troglodyte war continues, and a particu- larly offensive member of colony B is located 143 m below the top.
At what speed must a bomb be rolled to get him?
Answer in units of m/s
Explanation / Answer
A/. There will be no horizontal forces acting on the bomb in the horizontal direction, meaning no horizontal acceleration and therefore the horizontal velocity is constant. Therefore the time it takes to hit the opposite side of the cliff will be horizontal distance divided by horizontal velocity
= (46 m)/(5.2 m/s) = 8.85 s.
Now we turn our attention to the vertical direction. The vertical distance it travels, which is how far down the cliff it hits, is the distance it falls in 8.85 s. As the bomb leaves the cliff travelling horizontally, its initial vertical component of velocity is 0 m/s, and therefore the distance it has fallen as a function of time is d = 1/2 at² where a is the acceleration due to gravity. As this is equal to 9.8 m/s² the distance is d = 4.9t² and substituting the given value of t gives a distance of 383.45 m.
B/. First find the time it takes to fall 143 m. t² = 143/4.9 = 29.18 and taking the square root gives a time of 5.40 s.
So the bomb must travel a horizontal distance of 46m in a time of 5.40 s and therefore its horizontal velocity must be (46 m)/(5.40 s) = 8.52 m/s
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