A 4.5 kg block located on a horizontal frictionless floor is pulled by a cord that exerts a force F=13.50 N at an angle theta=30.0 degrees above the horizontal. What is the speed of the block 5.50 seconds after it starts moving?

Fhorizontal = 13.5 cos 30

m a = 13.5 cos 30

a = (13.5/4.5) cos 30

v = a t

v = [(13.5/4.5) cos 30 ] (5.5)

Well, well, well! Looks like Mr. Block is going on a road trip, huh? Let's do some calculations and find out his speed!

First things first, we need to figure out the net force acting on the block. To do that, we can break down the force into its horizontal and vertical components. The horizontal component would be F * cos(theta), and the vertical component would be F * sin(theta).

Now, since we're lucky dwarves and we have a frictionless floor, the only the horizontal component of the force will cause acceleration. So, we can use Newton's second law, which states that F = m * a, to find the acceleration.

Plugging in the values, we get a = (13.50 N * cos(30.0 degrees)) / 4.5 kg. Calculate that and you'll find the acceleration!

Now, let's get to the fun part - finding the speed! Since we're given the time, we can use the formula v = u + at, where u is the initial velocity, a is the acceleration, and t is the time.

Since the block starts from rest (poor thing), the initial velocity, u, is 0 m/s. Plug in the values for acceleration and time, and voila - you've got the speed!

So, grab your calculator and crunch those numbers. And remember, if math gets you down, I'm always here to clown around!

To find the speed of the block 5.50 seconds after it starts moving, we need to use the principles of Newton's laws of motion.

Step 1: Resolve the force into its horizontal and vertical components.
The horizontal component of the force can be found using the equation: F_horizontal = F * cos(theta)
F_horizontal = 13.50 N * cos(30.0°) = 13.50 N * 0.866 = 11.68 N

Step 2: Calculate the acceleration of the block.
The net force acting on the block can be determined using Newton's second law:
Net force = mass * acceleration
We can rearrange this equation to find the acceleration:
acceleration = Net force / mass

Since there is no friction in this scenario, the net force acting on the block is equal to the horizontal force:
acceleration = F_horizontal / mass
acceleration = 11.68 N / 4.5 kg = 2.6 m/s^2

Step 3: Determine the final velocity of the block after 5.50 seconds.
Using the equation for constant acceleration:
final velocity = initial velocity + (acceleration * time)

Since the block starts from rest, the initial velocity is zero:
final velocity = 0 + (2.6 m/s^2 * 5.50 s)
final velocity = 14.3 m/s

Thus, the speed of the block 5.50 seconds after it starts moving is 14.3 m/s.

To find the speed of the block 5.50 seconds after it starts moving, we can use Newton's second law of motion.

First, let's resolve the force F into its horizontal and vertical components. The horizontal component of the force is given by:
F_horizontal = F * cos(theta)
F_horizontal = 13.50 N * cos(30.0 degrees)
F_horizontal = 11.69 N

The vertical component of the force is given by:
F_vertical = F * sin(theta)
F_vertical = 13.50 N * sin(30.0 degrees)
F_vertical = 6.75 N

Since the block is on a frictionless floor, the horizontal force (F_horizontal) will only accelerate the block, while the vertical force (F_vertical) will not affect the motion of the block.

The net force acting on the block in the horizontal direction is given by:
Net force = ma
F_horizontal = ma

Where:
m = mass of the block
a = acceleration of the block

To find the acceleration of the block, we can use the formula:
a = F_horizontal / m

Substituting the values, we have:
a = 11.69 N / 4.5 kg
a = 2.60 m/s^2

Now, we can find the speed of the block 5.50 seconds after it starts moving using the equation of motion:
v = u + at

Where:
v = final velocity (speed)
u = initial velocity (speed)
a = acceleration
t = time

Assuming the block starts from rest (u = 0 m/s), we have:
v = 0 + (2.60 m/s^2)(5.50 s)
v = 14.3 m/s

Therefore, the speed of the block 5.50 seconds after it starts moving is 14.3 m/s.