I am working through an antiderivative question but there is one part of the answer I don't understand.Since raindrops grow as they fall, their surface area increases and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 and its downward acceleration is a = { 9 − 0.9 t if 0 ⩽ t ⩽ 10 0 if t &gt; 10 If the raindrop is initially 500 above the ground, how long does it take to fall?So, v ( t ) = − 9 t + .45 t 2 − 10 s ( t ) = − 4.5 t 2 + .15 t 3 − 10 t + 500And then punch in t = 10 s ( 10 ) = − 4.5 ( 10 ) 2 + .15 ( 10 ) − 10 ( 10 ) + 500 = 100It's the position result of a 100 I don't undertand. What is the 100 supposed to represent?

Question

I am working through an antiderivative question but there is one part of the answer I don&#039;t understand.Since raindrops grow as they fall, their surface area increases and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 and its downward acceleration is  a  =      {                            9          −          0.9          t                           if           0          ⩽          t          ⩽          10                                      0                           if           t          &amp;gt;          10                        If the raindrop is initially 500 above the ground, how long does it take to fall?So,   v  (  t  )  =  −  9  t  +  .45      t          2        −  10  s  (  t  )  =  −  4.5      t          2        +  .15      t          3        −  10  t  +  500And then punch in   t  =  10  s  (  10  )  =  −  4.5  (  10      )          2        +  .15  (  10  )  −  10  (  10  )  +  500  =  100It&#039;s the position result of a 100 I don&#039;t undertand. What is the 100 supposed to represent?

Mathias Patrick · Accepted Answer

Explanation:s(t)  is a function which denotes the position of raindrops at time t. When   t  =  0  ,, then   s  (  0  )  =  500.. This tells us that the raindrops start falling at 500 units. We find their position at 10 seconds when   t  =  10  ,, which we see is   s  (  10  )  =  100.. This tells us that at 10 seconds, the raindrops are 100 units above 0. However, the question ofIf the raindrop is initially 500 above the ground, how long does it take to fall?was not answered. If you would like to answer this question, then you need to set   s  (  t  )  =  0 and solve for t. This is a standard quadratic equation.

I am working through an antiderivative question but there is one part of the answer I don't understa

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