Question

Can someone help me ASAP please

Answer 1

Well, it's a quadratic, so it has to have 2 roots. 'Roots' meaning when its velocity is 0 or in this case, the ball hits the ground. So, let's just throw this into the quadratic equation. Remember, the quadratic equation is:

`x = (-b + √(b^2-4ac) )/(2a)`
and

`x = (-b - √(b^2-4ac) )/(2a)`

To plug values in, let's first rearrange the equation, so it's easier to plug in:

`h = -5t^2-10t+65`

Plug in (a = -5, b = -10, c = 65) and since we are solving for t, not x:

`0 = -5t^2-10t+65`

`t = (10+ √((-10)^2-4(-5)(65)) )/(2(-5))`
and

`t = (10+ √((-10)^2-4(-5)(65)) )/(2(-5))`

Solve:

`t = (10+ √(100+1300) )/(-10) = (10+ √(1400) )/(-10)`
and

`t = (10- √(100+1300) )/(-10) = (10- √(1400) )/(-10)`

Simplify:

`t = (10+37.42)/(-10) =-4.742`
and

`t = (10-37.42)/(-10) = 2.742`

Since time cannot be negative, your answer is the ball takes 2.742 seconds to hit the ground.