+42 If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 36t + 4.
A. quantity of 9 plus or minus square root of 65 all over 8
B. 9 plus or minus square root of 65 end root over 8
C. quantity of 9 plus or minus square root of 97 all over 8
D. 9 plus or minus square root of 97 end root over 8
+23251 When the football hits the ground, the value of h will be 0.
Solving: -16t2 + 36t + 4 = 0
Using the quadratic formula with a = -16 b = 36 c = 4:
t = [ -36 +/- sqrt( 362 - 4(-16)(4) ) ] / [ 2(-16) ]
t = [ -36 +/- sqrt( 1296 + 256 ) ] / [ -32 ]
t = [ -36 +/- sqrt( 1552 ) ] / [ -32 ]
t = [ -36 +/- sqrt(16)·sqrt(97) ] / [ -32 ]
t = [ -36 +/- 4·sqrt(97) ] / [ -32 ]
Dividing numerator and denominator by -4:
t = [ 9 +/- sqrt(97) ] / 8
Answer C.
