A car is towing a boat on a trailer. The driver starts from rest and accelerates to a velocity of +11 m/s in a time of 28 s. The combined mass of the boat and trailer is 410 kg. The frictional force acting on the trailer can be ignored. What is the tension in the hitch that connects the trailer to the car ?

Options

A. `3.2xx10^(2)N`
B. `1.6xx10^(2)N`
C. `6.5xx10^(2)N`
D. `4.0xx10^(3)N`

Answer

To solve the problem of finding the tension in the hitch that connects the trailer to the car, we can follow these steps:

### Step 1: Determine the acceleration of the car
We know that the car starts from rest and accelerates to a velocity of +11 m/s in a time of 28 seconds. We can use the first equation of motion:

\[ v = u + at \]

Where:
- \( v \) = final velocity = 11 m/s
- \( u \) = initial velocity = 0 m/s (starts from rest)
- \( a \) = acceleration
- \( t \) = time = 28 s

Rearranging the equation to solve for acceleration \( a \):

\[ a = \frac{v - u}{t} = \frac{11 \, \text{m/s} - 0 \, \text{m/s}}{28 \, \text{s}} \]

Calculating the acceleration:

\[ a = \frac{11}{28} \, \text{m/s}^2 \]

### Step 2: Calculate the tension in the hitch
According to Newton's second law of motion, the tension \( T \) in the hitch can be expressed as:

\[ T = m \cdot a \]

Where:
- \( m \) = combined mass of the boat and trailer = 410 kg
- \( a \) = acceleration calculated in Step 1

Substituting the values:

\[ T = 410 \, \text{kg} \cdot \frac{11}{28} \, \text{m/s}^2 \]

Calculating the tension:

\[ T = 410 \cdot \frac{11}{28} \]

\[ T = 410 \cdot 0.392857 \]

\[ T \approx 161.43 \, \text{N} \]

### Final Answer
The tension in the hitch that connects the trailer to the car is approximately **161.43 N**.

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