Question

A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in t seconds is given by s(t) = -16t^2 + 142t. At what time or times will the ball be 140 ft from the ground? round your answer to the nearest tenth, if necessary.

Answer 1

The ball will be 140 ft from the ground when t = 1.1s and when t = 7.7s

Explanation:

To solve this question, we need to understand how to solve a quadratic equation.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = (x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\bigtriangleup))/(2*a)`

`\bigtriangleup = b^(2) - 4ac`

The position of the pall is given by the following equation.

`s(t) = -16t^(2) + 142t`

At what time or times will the ball be 140 ft from the ground?

This is t when
`s(t) = 140`

So

`140 = -16t^(2) + 142t`

`16t^(2) - 142t + 140 = 0`

So

`a = 16, b = -142, c = 140`

`\bigtriangleup = b^(2) - 4ac = (-142)^(2) - 4*16*140 = 11204`

`t_(1) = (-(-142) + √(11204))/(2*16) = 7.7`

`t_(2) = (-(-142) - √(11204))/(2*16) = 1.1`

The ball will be 140 ft from the ground when t = 1.1s and when t = 7.7s