Question

A golfer hits a ball from a starting elevation of 6 feet with a velocity of 70 feet per second down to a green with an elevation of −3 feet. The number of seconds t it takes the ball to hit the green can be represented by the equation −16t2 + 70t + 6 = −3. How long does it take the ball to land on the green? It takes the ball seconds to land on the green.

Answer 1

The time it takes the ball to land on green is 4.4175 seconds

Explanation:

Given

Equation for number of seconds it take to hit the green: −16t² + 70t + 6 = −3

Required

The value of t.

The interpretation of this question is that, we should solve for t in the above equation.

-16t² + 70t + 6 = −3

Collect like terms

-16t² + 70t + 6 - 3 = 0

-16t² + 70t + 3 = 0

Multiply through by -1

-1(-16t² + 70t + 3) = -1 * 0

16t² - 70t - 3 = 0

Solving using quadratic formula.

`t = (-b+-√(b^2 - 4ac))/(2a)`

Where a = 16, b = -70, c = -3

t = (-(-70) ± √(-70² - 4 * 16 * -3))/(2 * 16)

`t = (-(-70)+-√((-70)^2 - 4 * 16 * -3))/(2 * 16)`

t = (70 ± √(4900 + 192))/32

`t = (70+-√(4900 + 192))/(32)`

`t = (70+-√(5092))/(32)`

`t = (70+-71.36)/(32)`

`t = (70+71.36)/(32)` or
`t = (70-71.36)/(32)`

`t = (141.36)/(32)` or
`t = (-1.36)/(32)`

`t = 4.4175 \\ or\\ t =-0.0425`

But t can't be negative.

So, t = 4.4175

The time it takes the ball to land on green is 4.4175 seconds