Question

A ball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t seconds after launch is given by $f(t) = -30t + 299$. The height of the ball 9 seconds after launch is feet. (Round answer to nearest tenth.) 

          A ball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t seconds after launch is given by $f(t) = -30t + 299$.
The height of the ball 9 seconds after launch is  feet.
(Round answer to nearest tenth.)
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A ball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t seconds after launch is given by f(t) = -30t + 299. The height of the ball 9 seconds after launch is feet. (Round answer to nearest tenth.)

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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A ball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t seconds after launch is given by v(t) = 301 + 299t. The height of the ball 9 seconds after launch is feet (Round answer to nearest tenth.)
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Transcript

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00:01 Hello students we are given here the ball is launched straight up in the air from the height this and velocity t second after the launch is given by ft is equal to minus 32t plus 288 we need to find the height of all after 9 seconds, so basically the answer we have to give in feet so what is our velocity function which is f t is equals to minus 32 t plus 288 and we all know if we want to calculate the height of all we need our height function.
00:39 So height function is basically integration of ft d t right so if i write for this this will come out as minus 32 t plus 288 and this will come out as d t right and this is integration of x -rich -to -power n d x is x is to our n plus 1 divided by n plus 1 plus constant term so if i write here this is minus 32 t squared divided by 2 plus 288 t right so basically if i write for this this will come out as minus 16 t square plus 288 t right plus constant term so basically this is also constant term we all know at t equals to zero height is 5 feet so at t equals to 0 h0 is basically 5 feet so what would be the answer regarding that then height function is basically h t is equal to minus 16 t square plus 288 t plus 5 so basically this is our height function so now if i write for this so here height of ball after 9 seconds.
02:04 So t equals to 9 seconds we need to write here.
02:09 This is h9 is equal to minus 16 multiplied by 81 plus 288 plus 288 plus this is 288 multiply by 9 plus 5...
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