Help with vectors and 2-dimentisonal motion: relative velocity

In summary, a science student on a train traveling at a constant speed of 10 m/s throws a ball at an angle of 60° with the horizontal. The student's professor sees the ball rise vertically and the problem can be solved using the Galilean transformation for inertial frames. By using the inverse of this principle, the magnitude of the ball's velocity in the moving frame can be calculated.
  • #1
xkamranx
2
0
A science student is riding on a flatcar of a train traveling along a straight horizontal track at a constant speed of 10 m/s. The student throws a ball along a path that he judges to make an initial angle of 60° with the horizontal and to be in line with the track. The student’s professor, who is standing on the ground nearby, observes the ball to rise vertically. How high does the ball rise?

Thanks a lot.
 
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  • #2
anyone haev any idea?
 
  • #3
The basic principle for this problem would be to use the Galilean transformation for inertial frames. In simpler words, if you know the velocity of an object in a moving frame, what is the velocity of that same object in a stationary frame?

Once you know this, you can use it's inverse into your problem. Knowing the apparent velocity in the stationary frame, what is the velocity in the moving frame?
 
  • #4
The train is moving with a speed of 10 m/s . The balls horizontal velocity is
[tex] v\sin{60} [/tex]. From the ground, the horizontal velocity is zero. Can you calculate the magnitude of the balls velocty from this?
 

FAQ: Help with vectors and 2-dimentisonal motion: relative velocity

What are vectors and how are they used in 2-dimensional motion?

Vectors are mathematical quantities that have both magnitude (size) and direction. In 2-dimensional motion, vectors are used to represent the displacement, velocity, and acceleration of an object in a plane. They allow us to analyze and understand the motion of objects in two dimensions.

How do you calculate the relative velocity between two objects?

The relative velocity between two objects is the difference in their velocities. In 2-dimensional motion, we can calculate it by subtracting the individual velocities of the objects in the x and y directions. This can be represented as a vector with a magnitude and direction.

What is the difference between speed and velocity?

Speed is a scalar quantity that represents how fast an object is moving, while velocity is a vector quantity that includes both speed and direction. In 2-dimensional motion, velocity is crucial as it tells us both how fast and in what direction an object is moving.

How do you use vectors to analyze projectile motion?

Projectile motion is a type of 2-dimensional motion where an object is launched into the air and moves along a curved path due to the force of gravity. Vectors are used to analyze this motion by representing the initial velocity, acceleration, and displacement of the object. By breaking down these vectors into their x and y components, we can determine the trajectory and final landing spot of the projectile.

Can vectors be used to solve real-world problems related to 2-dimensional motion?

Yes, vectors are widely used in solving real-world problems related to 2-dimensional motion, such as calculating the speed and direction of a moving vehicle, determining the displacement of an airplane with changing wind speeds, or predicting the path of a ball thrown by a pitcher. By using vectors, we can accurately model and analyze the motion of objects in the real world.

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