You are traveling in a convertible with the top down. The car is moving at a constant velocity of 17.5 m/s, due east along flat ground. You throw a tomato straight upward at a speed of 13.0 m/s. How far has the car moved when you get a chance to catch the tomato?

V = Vo + g*Tr = 0 @ max ht.

Tr = -Vo/g = -17.5/-9.8 = 1.79 s. = Rise
time.

Tf = Tr = 1.79 s. = Fall time.

Tr + Tf = 1.79 + 1.79 = 3.58 s = Time in
flight.

d = Vc*(Tr+Tf) = 17.5 * 3.58 = 62.7 m.

hf=hi+1/2 g t^2 + vit

hf, hi=0
t= 2vi/g

horizontal distance= t*17.5m/s

To answer this question, we need to consider the horizontal motion of the car and the vertical motion of the tomato separately.

First, let's analyze the horizontal motion. Since the car is moving at a constant velocity eastward, the distance it travels over time is given by:

Distance = Velocity × Time

In this case, the car's velocity is 17.5 m/s, and the time is unknown. Therefore, we'll refer to the time as 't' for now.

Now, let's focus on the vertical motion of the tomato. The tomato is thrown straight upward with an initial speed of 13.0 m/s. We know that the only force acting on the tomato in the vertical direction is gravity, which accelerates it downward at a rate of approximately 9.8 m/s^2.

To find the time it takes for the tomato to reach its highest point and fall down, we can use the following equation:

Vertical Displacement = Initial Vertical Velocity × Time + (0.5 × Acceleration × Time^2)

Since the tomato is thrown upward and comes back down, its vertical displacement is zero. The initial vertical velocity is 13.0 m/s, and the acceleration due to gravity is -9.8 m/s^2 (negative because it acts in the opposite direction to the initial velocity). Let's solve for 't' in this equation.

0 = 13.0 × t + 0.5 × (-9.8) × t^2

This equation is a quadratic equation, and we can solve it using the quadratic formula. However, since the tomato returns back to the same height, we know it will take the same time to reach the highest point as it will take to come back down. Therefore, we only need to consider the positive root of the quadratic equation.

By solving the equation, we find t ≈ 2.67 seconds.

Now, let's calculate the distance the car has traveled during this time. We already know the car's velocity is 17.5 m/s. Therefore, we can substitute the time 't' we found into the equation for distance:

Distance = Velocity × Time

Distance = 17.5 m/s × 2.67 s

Distance ≈ 46.7 meters

So, when you get a chance to catch the tomato, the car would have traveled approximately 46.7 meters.