1)A car of mass 1330 kg is traveling at 28.0 m/s. The driver applies the brakes to bring the car to rest over a distance of 79.0 m. Calculate the retarding force acting on the car.

I don't get it. What is retarding force? gravity has to factor in somewhere due to acceleration

(79.0/28.0)*1330
3752.5

2)What should be the angle between two vectors of magnitudes 3.20 and 5.70 units, so that their resultant has a magnitude of 6.10 units?

6.1 = sqrt(5.7 + 3.2cos(t)² + (3.2sin(t)²
37.21 = 35.69 + 36.48cos(t) + 7.04cos²(t)
7.04cos²(t) + 36.48cos(t) -1.52 = 0

98.2 im really confused

I don't know anything about physics -- but a retarding force must be the brakes that are applied because they the motion of the car.

You could have checked a dictionary for the definition of retarding.

When stopping, retarding force is friction. Brakes make the wheels slow, and the rubber acts on the road to slow vehicles. Gravity only assists friction.

2. Use the law of cosines. You have three sides, solve for the angle

1) Retarding force is the force acting in the opposite direction to the motion of an object, slowing it down or bringing it to rest. In this case, the retarding force is the force applied by the brakes of the car to slow it down.

To calculate the retarding force acting on the car, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:

Force = Mass × Acceleration

In this case, the car is initially traveling at 28.0 m/s and is brought to rest, so the final velocity is 0 m/s. The distance traveled is 79.0 m.

To calculate the acceleration, we can use the formula:

Acceleration = (Final Velocity - Initial Velocity) / Time

Since the time is not given in this problem, we'll use the equation:

Acceleration = (Final Velocity^2 - Initial Velocity^2) / (2 × Distance)

Acceleration = (0^2 - 28.0^2) / (2 × 79.0)

Acceleration = - 28.0^2 / (2 × 79.0)

Acceleration ≈ -9.95 m/s^2

Now, we can calculate the retarding force using the formula:

Force = Mass × Acceleration

Force = 1330 kg × (-9.95 m/s^2)

Force ≈ -13,217 N

Therefore, the retarding force acting on the car is approximately -13,217 N. The negative sign indicates that the force is acting in the opposite direction to the motion of the car.

2) To find the angle between two vectors with given magnitudes, we can use the dot product of the vectors.

The dot product of two vectors A and B is given by:

A · B = |A| |B| cos θ

In this case, the magnitudes of the vectors are given as 3.20 and 5.70 units, and the magnitude of the resultant vector is given as 6.10 units.

Using the given information, we have:

6.10 = √(3.20^2 + 5.70^2 - 2 × 3.20 × 5.70 cos θ)

Simplifying the equation, we get:

6.10^2 = 3.20^2 + 5.70^2 - 2 × 3.20 × 5.70 cos θ

37.21 = 35.69 + 36.48 cos θ - 7.04 cos^2 θ

Rearranging the equation, we have:

7.04 cos^2 θ - 36.48 cos θ + 1.52 = 0

Now we can solve this quadratic equation for cos θ using the quadratic formula:

cos θ = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 7.04, b = -36.48, and c = 1.52. Plugging these values into the quadratic formula, we get:

cos θ = (-(-36.48) ± √((-36.48)^2 - 4 × 7.04 × 1.52)) / (2 × 7.04)

Simplifying, we have:

cos θ = (36.48 ± √(1336.8704 - 42.1248)) / 14.08

cos θ = (36.48 ± √(1294.7456)) / 14.08

cos θ = (36.48 ± 35.98) / 14.08

Hence, we have two possible solutions:

1) cos θ = (36.48 + 35.98) / 14.08 = 5.76 / 14.08

2) cos θ = (36.48 - 35.98) / 14.08 = 0.50 / 14.08

Calculating the inverse cosine of each solution, we get:

θ = cos^(-1)(5.76 / 14.08) ≈ 65.12 degrees

θ = cos^(-1)(0.50 / 14.08) ≈ 84.20 degrees

Therefore, the angle between the two vectors should be approximately 65.12 degrees or 84.20 degrees.

1) Retarding force is the force that acts opposite to the direction of motion of an object, causing it to slow down or come to rest. In this case, it refers to the force applied by the brakes of the car to slow it down.

To calculate the retarding force, you can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the acceleration is the change in velocity over the distance the car comes to rest.

First, calculate the acceleration using the equations of motion:

v^2 = u^2 + 2as

Here, v is the final velocity (0 m/s), u is the initial velocity (28.0 m/s), a is the acceleration, and s is the distance (79.0 m).

Rearranging the equation, we have:

a = (v^2 - u^2) / (2s)
a = (0^2 - 28.0^2) / (2*79.0)

a = -28.0^2 / (2*79.0)
a = -0.45 m/s^2 (Note: the negative sign indicates that the acceleration is opposite to the initial velocity)

Next, use Newton's second law to calculate the force:

F = ma
F = 1330 kg * (-0.45 m/s^2)
F = -598.5 N

So, the retarding force acting on the car is -598.5 Newtons.

Regarding gravity, in this problem, we are only considering the retarding force caused by the brakes, and gravity is not directly involved. However, it's important to note that the car's weight (mg) would be acting downwards due to gravity, but since it's not related to the braking force, it is not considered in this calculation.

2) To find the angle between two vectors given their magnitudes and the magnitude of their resultant, you can use the cosine rule.

The cosine rule states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the magnitudes of those two sides times the cosine of the angle between them.

In this case, the magnitudes of the two vectors are 3.20 units and 5.70 units, and the magnitude of their resultant is 6.10 units. Let's assume the angle between the two vectors is denoted by "θ".

Applying the cosine rule, we have:

6.10^2 = 3.20^2 + 5.70^2 - 2(3.20)(5.70)cos(θ)

Simplifying:

37.21 = 10.24 + 32.49 - 36.48cos(θ)

Rearranging and combining like terms:

36.48cos(θ) = 45.46

Dividing both sides by 36.48:

cos(θ) = 45.46 / 36.48
cos(θ) ≈ 1.247

To find the angle θ, you can take the inverse cosine (cos^-1) of 1.247. However, since the value 1.247 is greater than 1, it is not a valid cosine value. Hence, there is no real angle that satisfies these conditions.

Please make sure to double-check your calculations to ensure accuracy.