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Answer :
Final answer:
The physics concepts used here include gravity, motion, and velocity. For a rock dropped from a 250m cliff, it takes approximately 3.19s to fall the first 50m and 0.72s to fall the last 50m. The bullet from the rifle travels at approximately 373m/s and to hit the target accurately, it should be aimed approximately 2.2cm above the target.
Explanation:
This question involves concepts of physics, specifically dealing with the topics of gravity, motion, and velocity both in projectiles and free-falling objects. The total time for a free-falling object can be calculated using the equation t = √(2d/g), where 'd' is the distance and 'g' is the acceleration due to gravity. The acceleration due to gravity is 9.8 m/s².
- For the rock being dropped from the cliff, (a) to calculate the time it will take to fall the first 50m, we plug into the equation and get t = √(2*50/9.8) ≈ 3.19 seconds. (b) The total time to fall 250m would be t = √(2*250/9.8) ≈ 7.13 seconds. To find the time it takes to fall the last 50m, we subtract the time it took to fall the first 200m (t= √(2*200/9.8) ≈ 6.41 seconds) from the total time, giving us approximately 0.72 seconds.
- For the rifle question, (a) to find the speed of the bullet, we first need to know the time it took to travel 25m. This can be found using the same fall time formula as above, with 'd' as the 2.2cm (or 0.022m). This gives us a time of about 0.067 seconds. The speed of the bullet is then 25/0.067 ≈ 373m/s. (b) To find the initial aim point for accuracy, we equate the horizontal motion with the vertical motion, yielding an aim height of approximately 0.022 m or 2.2 cm above the target.
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