If the back of the truck is 1.3 m above the ground and the ramp is inclined at 22 ∘, how much time do the workers have to get to the piano before it reaches the bottom of the ramp?

Refer to the diagram shown below.

Assume that

(a) The piano rolls down on frictionless wheels,

(b) Wind resistance is negligible.

The distance along the ramp is

d = (1.3 m) / sin (22°) = 3.4703 m

The component of the piano's weight along the ramp is

mg sin (22°)

If the acceleration down the ramp is a, then

ma = mg sin (22°)

a = g sin (22°) = (9.8 m/s²) sin (22°) = 3.671 m/s²

The time, t, to travel down the ramp from rest is given by

(3.4703 m) = 0.5 * (3.671 m/s²) * (t s) ²

t² = 3.4703/1.8355 = 1.8907

t = 1.375 s

Answer: 1.375 s