solve a math problem

Question

A 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.

Answer 1

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

Answer 2

384 = -16t² + 160t

Can you solve for t and answer?

Answer 3

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.