While a roofer is working on a roof that slants at 39.0 degrees above the horizontal, he accidentally nudges his 88.0 N toolbox, causing it to start sliding downward, starting from rest.

If it starts 4.90 m from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 18.0 N?

V = 6.974 m/s

Explanation:

Component (box) weight acting parallel and down roof 88 (sin39.0°) = 55.4 N

Force of kinetic friction acting parallel and up roof = 18.0 N

Fnet force acting on tool box acting parallel and down roof

Fnet = 55.4 - 18.0

Fnet=37.4 N

acceleration of tool box down roof

a = 37.4 (9.81) / 88.0

a = 4.169 m/s²

d = 4.90 m

t = √2d/a

t = √2 (4.90) / 4.169

t = 1.662 s

V = at

V = 4.169 (1.662)

V = 6.974 m/s