Kinematics problem -- Calculating where a dropped stone will hit a car

[physicslover12]

Homework Statement:

A dishonest woman Sues a poor innocent young man, claiming that he intentionally dropped (free fall) a stone from the top of a bridge which is 6.0 m above the ground, which damaged the trunk of her car. The complainant admits that she was driving at the maximum speed allowed of 100 km / h. You are called as an expert in this case (you are a physicist, right?). By making the necessary approximations, will you be able to save the young man ?

Relevant Equations:

Y=Yo+vot+0,5a(t^2)
X=Vot+Xo

0=6-4.9(t^2)
0=-27,7t+Xo
From the first equation,
T= 1.10s
From the second equation,
(Xo/27,7)=t
0=6-4.9((Xo/27,7)^2)
We solve for Xo = 30,65
Now, we have
X=-27,7t+30,65
If t=1,10
Then , -27,7(1,10)+30,65=0,18 which is not equal to 0.
Which means the stone hits the ground first.
Is my answer correct ?

 

[hutchphd]

If you would say exactly what it is you are trying to show, your question would be easier to answer.

 

[physicslover12]

If you would say exactly what it is you are trying to show, your question would be easier to answer.

Hi , thank you for helping me. I am trying to show that the stone didn’t hit the woman‘s car by calculating when did the stone hit the ground x=0 and y=0 (free fall) ,and by using that time to see if the car was at x=0. ( I am really sorry my english is very limited)

 

[hutchphd]

I think your idea is part correct. Think about the shape of the car and where the stone is said to have hit.

 

[haruspex]

There's not enough information here.
We are not told the height of the trunk, so knowing it is 6m from bridge to the ground is not helpful. Ok, so assume it means the drop to the top of the trunk is 6m.
Next, we don't know where the impact point on the car was (horizontally) when the stone was supposed to have been released. Alternatively, if we were told the length of the trunk and height of car roof above trunk we could calculate whether the stone was traveling fast enough to miss the roof but hit the trunk.

You calculated 1.10 s to drop that far, and how far the car moves in that time. You then found that same distance in a slightly different way, and because of the rounding errors got a difference of 0.18. I am at a loss to understand what you think that proves.
To improve precision, either keep more digits at each intermediate point or work algebraically until the last step, only plugging in numbers in one final calculation (allowing your calculator to carry lots of digits through). The algebraic approach has a lot of other benefits too.

 

[jbriggs444]

You've correctly converted 100 km/h to 27.7 meters per second. That gives the horizontal component of the velocity of the stone relative to the moving car. Can you calculate an estimate for the vertical component?