Answer:
The height is [tex]h = 0.5224 \ m[/tex]
Explanation:
From the question we are told that
The combined mass of the child and the sled is [tex]m = 58.0 \ kg[/tex]
The speed of the sled is [tex]u = 3.20 \ m/s[/tex]
Generally applying SOHCAHTOA on the slope which the combined mass is down from
Here the length of the slope(L) where the combined mass slides through is the hypotenuses
while the height(h) of the height of the slope is the opposite
Hence from SOHCAHTOA
[tex]sin (\theta) = \frac{h}{L}[/tex]
=> [tex]Lsin(\theta) = h[/tex]
Generally from the kinematic equation we have that
[tex]v^2 = u^2 + 2aL[/tex]
Here the u is the initial velocity of the combined mass which is zero since it started from rest
and a is the acceleration of the combined mass which is mathematically evaluated as
[tex]a = g * sin (\theta )[/tex]
[tex]v^2 = u^2 + 2 * g * sin (\theta )L[/tex]
=> [tex]2Lsin(\theta ) = \frac{v^2 - u^2 }{g}[/tex]
=> [tex]h = \frac{ v^2 - u^2}{2g}[/tex]
=> [tex]h = \frac{ 3.20^2 - 0^2}{2 * 9.8 }[/tex]
=> [tex]h = 0.5224 \ m[/tex]
