A 25.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 21.00 m. When she is partway down the slide, at a height h2 of 8.00 m, she is moving at a speed of 7.80 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).

The mechanical energy lost due to friction is 2,424.5 J

Explanation:

Given;

mass of the child, m = 25 kg

intial velocity of the child, u = 0

final velocity of the child, v = 7.8 m/s

initial position of the child, h₁ = 21 m

final position of the child, h₂ = 8 m

Let the energy lost due to heat = ΔE

ΔE + ΔK.E  + ΔP.E = 0

ΔE  +   ¹/₂m(v² - u²)  +  mg(h₂ - h₁) = 0

ΔE   +   ¹/₂ x 25(7.8² - 0)    +   25 x 9.8(8 - 21) = 0

ΔE   +  760.5 J   - 3185 J =

ΔE   -  2,424.5 J = 0

ΔE = 2,424.5 J

Therefore, the mechanical energy lost due to friction is 2,424.5 J

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west