a crate is pushed to the top of a frictionless inclined plane 15 m long with a force of 25 N.

If the crate weighs 125 N, how high is the inclined plane?

0.5 m
1 m
3 m
or
5 m

mgh=25*15

h= 25*15/125
h= 3m

W=F(cosx)d=mgh(potential energy)

25(cos0)(15)=375
mgh=(12.77)(9.8)h
375=125h
375/125=h
h=3

Work input is equal to work output (no friction)

W in = W out
F x d = F x d
25 x 15 = 125 x d
d = 3m

Well, let's break it down, shall we?

The force applied to push the crate up the inclined plane is 25 N, against the weight of the crate, which is 125 N.

Now, we need to do a little bit of math. If we divide the force applied (25 N) by the weight of the crate (125 N), we get a ratio of 1:5.

That means that for every 1-meter increase in height, the crate moves 5 meters along the inclined plane.

Since the inclined plane is 15 meters long, we divide that by 5 and get a resulting height of... 3 meters!

So, the answer is indeed 3 meters. Don't worry, it wasn't a tall tale.

To find the height of the inclined plane, we can use the concept of work and energy. The work done on an object is equal to the force applied multiplied by the displacement in the direction of the force.

In this case, the force applied is 25 N and the displacement is the length of the inclined plane which is 15 m. The work done on the crate is therefore:

Work = Force * Displacement
Work = 25 N * 15 m
Work = 375 N·m or 375 J (Joules)

Since the crate is being pushed up the inclined plane against gravity, the work done on the crate is equal to the change in potential energy of the crate. The potential energy of an object near the surface of the Earth is given by the equation:

Potential Energy = mass * gravitational acceleration * height

The weight of the crate is given as 125 N, which is equal to the mass of the crate multiplied by the gravitational acceleration (9.8 m/s^2). Rearranging the equation, we get:

Potential Energy = weight * height
Potential Energy = 125 N * height

Now, equating the work done on the crate to its change in potential energy:

375 J = 125 N * height

Solving for height:

height = 375 J / 125 N
height = 3 m

Therefore, the height of the inclined plane is 3 meters.