Answer:
4.8967m
Explanation:
Given the following data;
M = 0.2kg
∆p = 0.58kgm/s
S(i) = 2.25m
Ratio h/w = 12/75
Firstly, we use conservation of momentum to find the velocity
Therefore, ∆p = MV
0.58kgm/s = 0.2V
V = 0.58/2
V = 2.9m/s
Then, we can use the conservation of energy to solve for maximum height the car can go
E(i) = E(f)
1/2mV² = mgh
Mass cancels out
1/2V² = gh
h = 1/2V²/g = V²/2g
h = (2.9)²/2(9.8)
h = 8.41/19.6 = 0.429m
Since we have gotten the heigh, the next thing is to solve for actual slant of the ramp and initial displacement using similar triangles.
h/w = 0.429/x
X = 0.429×75/12
X = 2.6815
Therefore, by Pythagoreans rule
S(ramp) = √2.68125²+0.429²
S(ramp) = 2.64671
Finally, S(t) = S(ramp) + S(i)
= 2.64671+2.25
= 4.8967m
In this exercise we have to use the knowledge of momentum to calculate the distance, so we have:
[tex]4.8967m[/tex]
For this, we have to organize the information given in the statement as:
Firstly, we use conservation of momentum to find the velocity, will be:
[tex]\Delta p = M\\0.58kgm/s = 0.2V\\V = 0.58/2\\V = 2.9m/s[/tex]
Then from the conservation of energy we find that:
[tex]E(i) = E(f)\\1/2mV^2= mgh\\1/2V^2 = gh\\h = 1/2V^2/g = V^2/2g\\h = (2.9)^2/2(9.8)\\h = 8.41/19.6 = 0.429m[/tex]
From the height found we can use similarity of triangles to find what is missing, like this:
[tex]h/w = 0.429/x\\X = 0.429*75/12\\X = 2.6815\\S(ramp) = \sqrt{2.68125^2+0.429^2}\\S(ramp) = 2.64671\\= 2.64671+2.25= 4.8967m[/tex]
See more about momentum at brainly.com/question/4956182
