Question

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?

Answer 1

The student's question is about calculating the time it takes for an object (piano) to travel down an inclined plane using principles from physics, specifically the kinematics of uniformly accelerated motion.

Step-by-step explanation:

The student is asking about the time it takes for an object to travel down an inclined plane. This is a classic physics problem involving kinematics and can be solved by applying the equations of motion for uniformly accelerated motion. Given the height of the truck bed (1.3m) and the angle of the ramp (22 degrees), the acceleration of the piano can be calculated using the components of gravitational acceleration along the inclined plane.

To solve this, first, find the acceleration component along the ramp using the formula a = g ⋅ sin(θ), where g is the acceleration due to gravity (9.8 m/s2), and θ is the angle of the ramp. Then, use the formula d = (at2) / 2 to solve for the time t, where d is the vertical height the piano travels (1.3m).

Answer 2

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