Answer:
0.0102 m or 1 cm
Explanation:
Let g = 10m/s2
The potential energy of the shopping cart of the top of the hill is:
[tex]E_p = mgh = 30*9.8*2 = 600 J[/tex]
When the cart gets to the bottom of the hill, all this potential energy is converted to kinetic energy:
[tex]E_k = mv^2/2 = 600 J[/tex]
[tex]v^2 = \frac{600*2}{30} = 40[/tex]
[tex]v = \sqrt{39.2} = 6.324 m/s[/tex]
As the cart stop due to the stump, the can of peaches flies with the same speed.
By Newton's 3rd law, the car would exert a 490N force on the can too
The deceleration of the can would then be:
[tex]a = F/m = 490/0.25 = 1960 m/s^2[/tex]
This force would stop the can, but not without making a dent, aka a traveled distance on the car skin
We can use the following equation of motion to find out the distance traveled by the can:
[tex]v^2 - v_0^2 = 2a\Delta s[/tex]
where v = 0 m/s is the final velocity of the can when it stops, [tex]v_0^2[/tex] = 40m/s is the initial velocity of the can when it hits, a = -1960 m/s2 is the deceleration of the can, and [tex]\Delta s[/tex] is the distance traveled, which we care looking for:
[tex]0 - 40 = 2*(-1960)*\Delta s[/tex]
[tex]\Delta s = \frac{40}{2*1960} = 0.0102 m[/tex] or 1 cm
