An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 212 N, toward east, on the boat. due to the angle of the sail, the wind causes the boat to slide in a straight line for a distance of 7.0 m in a direction 20° north of east. What is the kinetic energy of the iceboat at the end of that 7.0 m?

Work done on the boat= force*distane*cos20.
Set that equal to KE

Well, isn't that an interesting situation! Let's calculate the kinetic energy of the iceboat and find out!

First, let's find the work done on the boat. We'll use the formula "work = force * distance * cos(angle)". Plugging in the given values, we have:

Work = 212 N * 7.0 m * cos(20°)

Now, let's solve this equation and find out the work done on the boat.

(Running the calculations...)

Ah, according to my calculations, the work done on the boat is equal to approximately 1449.67 J (Joules).

Since work done is equal to the kinetic energy (KE), we can say that the kinetic energy of the iceboat at the end of the 7.0 m distance is approximately 1449.67 J.

Now that's what I call an "ice-tacular" amount of kinetic energy! Stay cool!

To find the kinetic energy (KE) of the iceboat at the end of the 7.0 m distance, we can use the formula KE = work done on the object.

Given:
Force exerted by the wind (F) = 212 N
Distance traveled (d) = 7.0 m
Angle North of East (θ) = 20°

First, we need to calculate the work done on the boat by the wind. The work done can be found using the formula: Work = Force * Distance * cos(θ).

Work = 212 N * 7.0 m * cos(20°)

To calculate the value, first convert the angle from degrees to radians because the trigonometric functions in most programming languages/ calculators require input in radians.

θ (in radians) = 20° * (π / 180°) ≈ 0.3491 radians

Now, substitute the values into the formula:

Work = 212 N * 7.0 m * cos(0.3491 radians)

Work ≈ 1286.48 J (rounded to two decimal places)

Therefore, the work done on the boat by the wind is approximately 1286.48 J.

Finally, the kinetic energy of the iceboat at the end of the 7.0 m distance is equal to the work done:

KE = 1286.48 J

So, the kinetic energy of the iceboat at the end of the 7.0 m distance is approximately 1286.48 J.

To find the kinetic energy (KE) of the iceboat at the end of the 7.0 m distance, we need to calculate the work done on the boat and then set it equal to the kinetic energy.

The work done on an object is given by the formula:

Work = Force * Distance * cos(θ)

In this case, the force acting on the boat is the constant force of 212 N, and the distance the boat slides is 7.0 m. The angle θ is the angle between the direction of the force and the direction of the displacement.

From the question, we are told that the direction of the boat's motion is 20° north of east. So the angle between the force and the displacement is the complement of this angle, which is 70°. Therefore:

Work = 212 N * 7.0 m * cos(70°)

Now, use a calculator to compute the trigonometric function of cos(70°) and multiply it by 212 N * 7.0 m to find the value of work done on the boat.

Finally, set this value equal to the kinetic energy of the iceboat:

Work = KE

Solve the equation for KE to find the kinetic energy of the iceboat at the end of the 7.0 m distance.