A ball is thrown from an initial height of 3 feet with an initial upward velocity of 44 ft/s. The ball's height h (in feet) after seconds is given by the following. h = 3+4…

Question

asked May 9, 2023 121k views

2 Answers

Mcnarya · Answer 1 · 2023-05-11T08:51:41+0000

Answer:

t = 2.175 s (3 dp)

t = 0.575 s (3 dp)

Explanation:

Given equation:
h=3+44t-16t^2

To find all values of t for which the ball's height is 23 ft, substitute h = 20 into the equation and solve for t:

$\implies h=23$

$\implies 3+44t-16t^2=23$

$\implies 16t^2-44t-3+23=0$

$\implies 16t^2-44t+20=0$

Factor out common term 4:

$\implies 4(4t^2-11t+5)=0$

Divide both sides by 4:

$\implies 4t^2-11t+5=0$

Quadratic formula

$x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when}\:ax^2+bx+c=0$

Use the quadratic formula to solve for t:

$\implies t=(-(-11) \pm √((-11)^2-4(4)(5)) )/(2(4))$

$\implies t=(11 \pm √(41))/(8)$

Therefore,

Yue Lin Ho · Answer 2 · 2023-05-15T21:17:38+0000

Answer:

See below ↓↓

Explanation:

Given function

We need to calculate the possible values of t at h = 23 feet.

Subsituting h = 23,

Solving for 't' using quadratic formula

Solutions