A ball is tossed upward from the ground. Its height

Rivka Thorpe

Rivka Thorpe

Answered question

2021-08-11

A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function h(t)=16t2+24t. Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.

Answer & Explanation

Viktor Wiley

Viktor Wiley

Skilled2021-08-12Added 84 answers

Comparing h(t)=16t2+24t with ax2+bx+c, we have a=16.b=24. 
b2a=242(16) 
24 and 16 are multiples of 2.
242(16)=2×2×2×32×2×2×2×2=34 
Find h(34).
h(34)=16(34)2+24(34) 
h(34)=2×2×2×2×(3×34×4)+2×2×2×3(34) 
h(32)=2×2×2×2(3×32×2×2×2)+2×2×2×3(32×2) 
h(32)=3×3+2×3×3 
h(32)=9+18=9 
b2a=34 and h(b2a)=9
The vertex is (34,9) , and it took 0.75 seconds for the ball to reach the ground. 
Answer: The maximum height of the ball is 9 feet and it took 34 or 0.75 seconds for the ball to reach the ground.

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