Kinematics 2D: Solve Initial Speed of Cork

In summary, the problem involves a cork being shot out of a champagne bottle at an angle of 38.0 degrees above the horizontal. The cork travels a horizontal distance of 1.4m in 1.15 seconds. The equation x(t)=x2+vit+.5at2 is used to find the initial speed. However, the solution is incorrect because it neglects the y component of the motion and does not use the given angle. The correct approach would be to break down the equation into x and y components and solve for the initial speed using the given information.
  • #1
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Homework Statement


A cork shoots out of a champagne bottle at an angle of 38.0 degrees above the horizontal. If the cork travels a horizontal distance of 1.4m in 1.15 seconds what was the initial speed?


Homework Equations


x(t)=x2+vit+.5at2


The Attempt at a Solution



1.4=0+1.15x

x=1.217

However, this is wrong, hence the asking for help. I'm really wondering if I'm using the wrong formula or just missing something obvious.
 
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  • #2
Hello,

Yeah, like you said, that's wrong :P

Your formula is the right idea though. Usually with this problem, they tell you something like, "A ball is shot out of a cannon at an angle x with an initial speed of v0. How long does it take to hit the ground, and how far does it go?" And then you work through it by calculating the y component of the motion (which is affected only by gravity) to find the time, and then plug that time into the x version of the equation to find the distance. Because the full equation is:

s(t) = s0 + v0t + 1/2at^2 , which you can break down into the x and y components:

y(t) = y0 + v0yt + 1/2ayt^2 and
x(t) = x0 + v0xt +1/2axt^2,

where you know that the acceleration in the y-axis is due solely to gravity (ay = g), and the acceleration in x is 0 (these problems typically neglect friction).

Here, however, you've been given the angle, the horizontal distance, and the time already, and all you have to do is find the initial speed.

Your solution is incorrect because you neglected the y component of the motion. IE, you solved your equation for the x component only, as if it had been shot at an angle of zero and there were no gravity.

A clue for you should have been (probably was, but you weren't sure what to do with it) the fact that you didn't use the 38 degrees anywhere. You will need this number.

Hope this helps, write again if you're not sure how to proceed!
 
  • #3


Dear student,

Thank you for your question. It seems like you are on the right track with using the kinematic equation x(t) = x0 + v0t + 1/2at^2 to solve for the initial speed of the cork. However, it appears that you may have made a mistake in your calculations. Let me walk you through the correct approach.

First, let's define our variables:
x0 = initial horizontal distance (in this case, 0)
v0 = initial speed (what we are trying to solve for)
t = time (1.15 seconds, given in the problem)
x = final horizontal distance (1.4m, given in the problem)
a = acceleration due to gravity (we will assume this to be -9.8 m/s^2 since the cork is being shot upwards)

Next, let's plug these values into our kinematic equation:
x(t) = x0 + v0t + 1/2at^2
1.4 = 0 + v0(1.15) + 1/2(-9.8)(1.15)^2
1.4 = 1.15v0 - 6.697
1.4 + 6.697 = 1.15v0
8.097 = 1.15v0
v0 = 8.097/1.15
v0 = 7.04 m/s

Therefore, the initial speed of the cork was 7.04 m/s. I hope this explanation helps you understand the correct approach to solving this problem using kinematics. Keep up the good work!

Best,
 

1. What is Kinematics 2D?

Kinematics 2D is a branch of physics that deals with the motion of objects in two-dimensional space. It involves studying the position, velocity, and acceleration of objects as they move in a plane.

2. How is initial speed of a cork solved in Kinematics 2D?

The initial speed of a cork can be solved using the kinematic equations, which relate the initial velocity, final velocity, acceleration, and displacement of an object. These equations can be used to calculate the initial speed of a cork based on its displacement and acceleration.

3. What is the importance of solving initial speed of a cork in Kinematics 2D?

Solving the initial speed of a cork in Kinematics 2D is important because it allows us to understand the motion of the cork and predict its future position and velocity. This information can be useful in various applications, such as determining the trajectory of a cork in a game of darts or predicting the landing point of a cork in a bottle.

4. What are the key factors that affect the initial speed of a cork in Kinematics 2D?

The key factors that affect the initial speed of a cork in Kinematics 2D are the initial position, displacement, acceleration, and time. These factors determine the velocity of the cork at any given time and can be used to calculate its initial speed.

5. How can Kinematics 2D be applied to real-life situations?

Kinematics 2D can be applied to real-life situations in various fields, such as sports, engineering, and transportation. For example, it can be used to study the trajectory of a baseball in a game, design the motion of a roller coaster, or calculate the landing distance of an airplane.

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