You are traveling in a car with convertible roof with the top down. The car is moving at a constant velocity of 25 m/s, due east along flat ground. You throw a tomato straight upward at a speed of 11 m/s. How far has the car moved when you get a chance to catch the tomato?

Options

A. 66 m
B. 44 m
C. 56 m
D. 28 m

Answer

To solve the problem step by step, we need to analyze the motion of the tomato and the car separately, and then combine the results to find out how far the car has moved when the tomato comes back down to the same height.

### Step 1: Determine the time the tomato is in the air.
The tomato is thrown straight upward with an initial velocity of 11 m/s. To find out how long it takes for the tomato to go up and come back down, we can use the following kinematic equation for vertical motion:

\[ h = ut + \frac{1}{2} a t^2 \]

Where:
- \( h \) is the maximum height (which will be 0 when it returns to the original height),
- \( u \) is the initial velocity (11 m/s),
- \( a \) is the acceleration due to gravity (-9.8 m/s², acting downwards),
- \( t \) is the total time in the air.

At the maximum height, the final velocity will be 0. We can use the formula:

\[ v = u + at \]

Setting \( v = 0 \) (at the peak height):

\[ 0 = 11 - 9.8t \]

Solving for \( t \):

\[ 9.8t = 11 \implies t = \frac{11}{9.8} \approx 1.12 \text{ seconds (time to reach maximum height)} \]

The total time in the air will be double this (up and down):

\[ t_{total} = 2 \times 1.12 \approx 2.24 \text{ seconds} \]

### Step 2: Calculate the distance traveled by the car.
The car is moving at a constant velocity of 25 m/s. To find out how far the car travels during the time the tomato is in the air, we can use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values we have:

\[ \text{Distance} = 25 \, \text{m/s} \times 2.24 \, \text{s} \approx 56 \, \text{meters} \]

### Conclusion
The car moves approximately 56 meters while the tomato is in the air.

### Summary of Steps:
1. Calculate the time the tomato is in the air using kinematic equations.
2. Use the car's speed and the time to calculate the distance traveled by the car.