### Understanding the Motion of a Toy Car on an Inclined Ramp#### Problem StatementA toy car is rolling down the ramp as shown in the figure. The car's mass is \( m = 1.2 \) kg and the ramp makes an angle of \( \theta = 16 \) degrees with respect to the horizontal. Assume the car is rolling without friction.#### Objective Using the coordinate system specified (where the ramp is aligned with the x-axis), give an expression for the acceleration of the car in terms of \( \theta \), \( g \), and the unit vectors \( \vec{i} \) and \( \vec{j} \).#### Diagram DescriptionThe figure illustrates a toy car on an inclined ramp. The ramp is tilted at an angle \( \theta = 16 \) degrees above the horizontal. The coordinate system has the x-axis aligned with the surface of the ramp and the y-axis perpendicular to the ramp.- **x-axis**: Along the surface of the ramp.- **y-axis**: Perpendicular to the surface of the ramp. An arrow indicates the direction of the car's motion, which is downward along the ramp.#### Input Box and Virtual KeyboardTo calculate the acceleration \( \vec{a} \), input your answer using the provided virtual keyboard. The keyboard includes trigonometric functions, Greek letters, and unit vectors.#### Example InputTo input the expression for acceleration, you might use terms like \( g \sin(\theta) \vec{i} \) to represent the component of gravitational acceleration along the ramp. Use the given numeric keypad to fill in your answers and ensure correctness.For instance, the acceleration \( \vec{a} \) could be expressed as:\[ \vec{a} = g \sin(\theta) \vec{i} \]You can enter this into the input box using the virtual keyboard provided.#### Interaction Options- **Submit**: To check your answer.- **Hint**: To view a hint if you are stuck.- **I give up!**: To reveal the answer.Understanding the components of gravitational force along an inclined plane is crucial in solving this problem. Remember that the gravitational force has a component parallel to the ramp that causes the car to accelerate downward. Use the coordinate system and trigonometric identities to express this force appropriately.

Given, Mass, m =1.2 kg θ =16°

A toy car is rolling down the ramp as shown in the figure. The car's mass is m 1.2 kg and the ramp makes an angle of 8-16 degrees with respect to the horizontal. Assume the car is y₁ rolling without friction.

A toy car is rolling down the ramp as shown in the figure. The car's mass is m 1.2 kg and the ramp makes an angle of 8-16 degrees with respect to the horizontal. Assume the car is y₁ rolling without friction.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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