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Review Conceptual Example 5 before beginning this problem. You are traveling in a convertible with the top down. The car is moving at a constant velocity of 25 m/s, due east along flat ground. Youthrow 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?

56$m$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

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04:01

2D kinematics is the study…

10:12

A vector is a mathematical…

04:20

Review Conceptual Example …

03:04

In preparation for this pr…

01:41

02:16

Refer to Multiple-Concept …

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04:21

Before working this proble…

06:11

Before starting this probl…

03:52

Velocity and Acceleration …

02:27

Multiple-Concept Example 4…

01:58

See Sample Problem $F$ A …

01:32

04:31

08:25

$. .$ REFERRING TO CONCEPT…

02:05

A flat railroad car is mov…

00:37

02:23

A car is moving at constan…

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03:09

Consult Conceptual Example…

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02:45

Solve each problem. See Ex…

So the question states that a person riding in a car that's moving at 25 meters per second throws the tomatoes straight up in the air, 11 meters per second. And we're trying to find how far the car moves in the time that the tomatoes in the air. So we know that because the tomato is moving at 25 meters per second in the horizontal direction and so is the car. Ah, we really only need to focus on the vertical aspect of the tomato. Uh, tomato is always gonna land back in the car because they're moving at the same speed in the X direction. So to find the time that the tomato is in the air, we can use the que no magic formula, which states that the change in displacement is equal to the initial velocity time to the time plus 1/2 times the acceleration times of time squared. We know that the displacement of the tomato is going to be zero because it starts in the car and it ends in the car. We also know that the initial velocity is 11 meters per second and we could multiply this by the time we add 1/2 times the acceleration which in this case is negative 9.8 due to gravity and we multiply this by a T Square. So now we can solve for T so we can add, uh, 9.8 over to he squared We live in T so we added 9.8 it over to times t squared on both sides. And so now we can divide by t on both sides. We get 9.8 by two t equals 11 and then we divide by 9.8 or two on both sides and we get t it's equal to 22/9 20.8, which is just the same thing as 22.24 seconds. Now that we know the time, we can figure out how far the car has traveled. Based on the formula, Delta X equals V, not tea. And we know that the initial horizontal velocity of the car is 25 meters per second. Wilson, at the time that Thea tomatoes in the air is 22.24 meters seconds. So our total, um displacement is approximately equal to 56 meters. That's the answer

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