Question

A ball is thrown from an initial height of 5 feet with an initial upward velocity of 23/fts. The ball's height h (in feet) after tseconds is given by the following.h=5+23t - 16t2Find all values of t for which the ball's height is 13 feet.

Answer 1

x₂ = 0,59 sec

x₁ = 0,8475 sec

Explanation:

h(t) = -16*t² + 23*t + 5

h(t) is the trajectory of the ball, the curve is a parable opens downwards

if we force h(t) = 13 feet, we get;

h(t) = 13

13 = -16*t² + 23*t + 5 ⇒ -16*t² + 23*t - 8 = 0

or 16*t² - 23*t + 8 = 0

The above expression is a second degree equation, we proceed to solve it for t

x = [ 23 ± √529 - 512 ] /32

x = [ 23 ± √17 ] /32

x₁ = [ 23 + 4,12 ]/32 ⇒ x₁ = 27,12/32 ⇒ x₁ = 0,8475 sec

x₂ = [ 23 - 4,12 ]/32 ⇒ x₂ = 18,88 /32 ⇒ x₂ = 0,59 sec