Peter R. answered 08/23/23
Experienced Instructor in Prealgebra, Algebra I and II, SAT/ACT Math.
Why not divide 16t2 - 160t + 384 = 0 by 16?
t2 - 10t + 24 = 0 and factor.
(t - 4)(t - 6) = 0
So t = 4 or t = 6 sec
Beauty S.
asked 08/23/23A ball is thrown vertically in the air with a velocity of 160ft/s. Use the projectile formula h=−16t^2+v₀t to determine at what time(s), in seconds, the ball is at a height of 384ft.
Peter R. answered 08/23/23
Experienced Instructor in Prealgebra, Algebra I and II, SAT/ACT Math.
Why not divide 16t2 - 160t + 384 = 0 by 16?
t2 - 10t + 24 = 0 and factor.
(t - 4)(t - 6) = 0
So t = 4 or t = 6 sec
Mark M. answered 08/23/23
Mathematics Teacher - NCLB Highly Qualified
384 = -16t2 + 160t
Can you solve for t and answer?
Patrick A. answered 08/23/23
Retired Actuary and Excel Power User
The original expression 384 = -16t2 + 160t can be converted to 16t2 - 160t + 384 = 0, which allows the use of the quadratic formula
t = [ -b +/- SQRT( b2 - 4ac) ] / [ 2a ] = [ 160 +/- SQRT( 1602 - 4(16)384) ] / 32 = 5 +/- [SQRT(1024)]/[32]
t =5 +/- 1, or 4 and 6. Using the original expression, for t=4 we get -16(4*4) + 160*4 = -256 + 640 = 384,
and for t=6 we get -16(6*6) + 160 * 6 = -576 + 960 = 384, so both solutions are valid.
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