Selena is standing on a rock cliff that is 52 feet high. She tosses a pebble upward over the edge, where it hits the top of a 12 foot high boulder. The quadratic equation that models the path of the pebble is given below. How long did it take for the pebble to hit the top of the boulder? p(t)=-16t^2+12t+52
2 answers
Question:
Selena is standing on a rock cliff that is 52 feet high. She tosses a pebble upward over the edge, where it hits the top of a 12 foot high boulder. The quadratic equation that models the path of the pebble is given below. How long did it take for the pebble to hit the top of the boulder? p(t)=-16t^2+12t+52
Answers
Answer: At [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.Step-by-step explanation:Since we have given that Distance at which Selena is standing on a rock cliff = 52 feetHeight of boulder above a rock cliff = 12 footSo, the given quadratic equation would be [tex]p(t)=-16t^2+12t+52[/tex]First we derivative it w.r.t t,[tex]p'(t)=-32t+12[/tex]Now, we will find the critical value,[tex]-32t+12=0\\\\-32t=-12\\\\t=\dfrac{12}{32}=\dfrac{6}{16}=\dfrac{3}{8}[/tex]Now, we will check whether it is maximum or not.[tex]p''(t)=-32<0[/tex]So, we get that it is maximum.Hence, at [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.
Answer:The answer is t=3/8
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