Question
(a) Find the sum of the first 200 natural numbers.
(b) A golfball is dropped from a height of 30 ft to the pavement. It always rebounds three fourths of the (4)
distance that it drops. How far (up and down) will the ball have traveled when it hits the pavement for
the 6th time?
(b) A golfball is dropped from a height of 30 ft to the pavement. It always rebounds three fourths of the (4)
distance that it drops. How far (up and down) will the ball have traveled when it hits the pavement for
the 6th time?
Ask by Bradley Schofield. in South Africa
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) The sum of the first 200 natural numbers is 20,100.
(b) The golf ball travels approximately 167.29 feet up and down by the 6th hit.
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The Deep Dive
To find the sum of the first 200 natural numbers, you can use the formula
. So, for
, it becomes
. Voilà! The sum is 20,100!
Now, let’s break down the golf ball’s journey. On the first drop, it travels 30 ft down. It rebounds
ft up, then drops again, traveling 22.5 ft down. This pattern continues: the distance traveled forms a series. By the time it hits the pavement the 6th time, you total the distances for each drop and rebound, which calculates to 134.25 ft down and up combined!