Discrepancy with Toricellis equation in a 2D kinematics prob

• CherryWine
In summary, the problem involves a stone being thrown from a height of 2.1m with an angle of 45 degrees, and it lands 42m away from the throwing position. The initial velocity is 19.81 m/s and the flight time is 3s. The task is to find the maximum height using kinematics equations. By plugging in the variables into the equation y(t) and equating the final velocity to 0, the correct result of 10m from the starting position and 12.1m from the ground was obtained. However, when using the equation Vfin^2=V0^2+2gΔy and not considering the y-components of velocity, a result of
CherryWine

Homework Statement

A stone is thrown from a height 2.1m with an angle of 45 degrees. It fell to the ground 42 m from the throwing position, measured horizontally. Initial velocity is 19,81 m/s, flight time is 3s what is the maximum height?

Homework Equations

All 2D kinematics equations.

The Attempt at a Solution

I plugged in the variables into the equation y(t), and equated Vfin=0, for the maximum height and obtained the correct result which should be 10m from the starting position and 12,1m from the ground. But when I tried to solve the problem using equation Vfin^2=V0^2+2gΔy I obtain 20m which is not correct. Why is it not correct?

CherryWine said:
But when I tried to solve the problem using equation Vfin^2=V0^2+2gΔy I obtain 20m which is not correct. Why is it not correct?

You will need to show more of your work in order for us to find the error. Are the velocities in this equation supposed to be y-components of velocity?

TSny said:
You will need to show more of your work in order for us to find the error. Are the velocities in this equation supposed to be y-components of velocity?

Thank you very much! It was my careless mistake. I didn't use y-components of velocity. Thank you! Turns out to be consistent. Thanks again.

What is the Toricelli's equation and how is it used in 2D kinematics problems?

The Toricelli's equation, also known as the Torricelli's law, is a physics equation that describes the relationship between the initial velocity, acceleration, and displacement of an object in free fall. It is often used in 2D kinematics problems to calculate the distance traveled by an object in a certain amount of time.

What is the discrepancy with Toricelli's equation in a 2D kinematics problem?

The discrepancy with Toricelli's equation in a 2D kinematics problem arises when the object is not in free fall and is instead moving in a curved path. In this case, the equation does not accurately describe the motion of the object and can lead to incorrect calculations.

Why does the Toricelli's equation not work in 2D kinematics problems with curved motion?

The Toricelli's equation assumes that the object is moving in a straight line, which is not the case in 2D kinematics problems with curved motion. This leads to a discrepancy between the predicted and actual distance traveled by the object.

How can the discrepancy with Toricelli's equation be minimized in 2D kinematics problems?

The discrepancy with Toricelli's equation can be minimized by breaking down the curved motion into smaller, straight-line segments and using the equation for each segment. This will provide a more accurate estimation of the object's distance traveled.

Are there any alternative equations that can be used in 2D kinematics problems with curved motion?

Yes, there are alternative equations such as the equations of motion for projectile motion and circular motion that can be used in 2D kinematics problems with curved motion. These equations take into account the curved path of the object and provide more accurate results.

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