20.) A piano has been pushed to the top of the ramp at the back of a moving van. The workers think it is safe, but as they walk away, it begins to roll down the ramp.

If the back of the truck is 1.5 above the ground and the ramp is inclined at 29, how much time do the workers have to get to the piano before it reaches the bottom of the ramp?

Well, this situation sounds like a real-life version of a circus act! I hope those workers have their running shoes on! Now, let's get to the calculations.

To determine how much time the workers have, we need to calculate the time it takes for the piano to roll down the ramp. We can use the equation:

t = sqrt(2h/g)

Where:
t represents time,
h represents the vertical displacement (the height difference between the back of the truck and the ground),
and g represents the acceleration due to gravity.

In this case, the vertical displacement (h) can be calculated using basic trigonometry:

h = sin(29) * 1.5

Now, let's plug in the values and calculate the time:

t = sqrt(2 * (sin(29) * 1.5) / 9.8)

Calculating this equation will give us the approximate time the workers have to reach the piano before it reaches the bottom of the ramp. However, keep in mind that this is just an estimate and real-life scenarios can have other factors to consider.

So, my dear workers, I suggest you start running as fast as a track star because time's ticking! Good luck!

To find the time the workers have to get to the piano before it reaches the bottom of the ramp, we can use basic concepts from physics. In this scenario, we will assume there is no friction between the piano and the ramp.

First, let's break down the problem and gather the given information:
- Height of the back of the truck above the ground (H) = 1.5 meters.
- Incline angle of the ramp (θ) = 29 degrees.

Now, we can analyze the situation and use trigonometry to find the length of the ramp (L) using the given information:
- The height of the back of the truck (vertical component) forms a right triangle with the length of the ramp (hypotenuse) and the vertical distance traveled by the piano.
- Considering the trigonometric function sine (sin), we have sin(θ) = opposite/hypotenuse.
- Substituting the values, sin(29) = H/L, we can solve for L.

L = H / sin(θ)
L = 1.5 / sin(29)
L ≈ 3.064 meters

Now, we need to calculate the time it takes for the piano to reach the bottom of the ramp. To do this, we can use the kinematic equation for distance traveled (d) in terms of time (t) under constant acceleration due to gravity:

d = (1/2) * g * t^2

In this case, the distance traveled (d) is equal to the length of the ramp (L), and the acceleration due to gravity (g) is approximately 9.8 m/s^2.

L = (1/2) * g * t^2
3.064 = (1/2) * 9.8 * t^2
3.064 = 4.9 * t^2
t^2 = 3.064 / 4.9
t^2 ≈ 0.6253
t ≈ √0.6253
t ≈ 0.7915 seconds

Therefore, the workers have approximately 0.7915 seconds to get to the piano before it reaches the bottom of the ramp.

In the real world, a piano has considerable weight and therefore friction, which would reduce the net force, and acceleration down the plane.

Ignoring friction,
weight down the plane mg*cos29.

weight down the plane=m*a
a= g*cos29

vf= sqrt (2ad)=sqrt (2*a*1.5/sin29)

60 s