Calculating Maximum River Crossing Distance with Initial Velocity of 30 m/s

In summary, to determine the widest river a ball with an initial speed of 30 m/s can cross, you need to first split the initial velocity into vertical and horizontal components. Then, use the equation y=vyt-0.5gt2 to find the time for the vertical motion. Next, use the equation R=vxt to find the range, which will give you the distance that the ball can travel horizontally. This distance will represent the width of the river. To solve for the time in the vertical motion, you will need to use both the x and y components of the initial velocity.
  • #1
stressedgirl
13
0

Homework Statement


If you can hurl a ball so that its initial speed is 30 m/s, what is the widest river it can cross?

v1 = 30m/s

Homework Equations


I am not sure with only the one variable given.

The Attempt at a Solution


Start with a x and y component diagram?
 
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  • #2
Yes split the inital velocity into vertical and horizontal components.

Now consider vertical motion, when the ball lands on the ground again, the displacement is zero. Use y=vyt_0.5gt2 to get the time for this motion.

Now horizontally the Range (how wide your river is) is given by R=vxt

that 't' in the equation for 'R' is the time for the motion above.
 
  • #3
Umm.. I don't understand. How would the 't' answer the question? Wouldn't I need a 'd' since it's asking how wide the river could be?

edit: SOrry I don't really understand what I'm even supposed to draw in the diagrams of the components
 
  • #4
stressedgirl said:
Umm.. I don't understand. How would the 't' answer the question? Wouldn't I need a 'd' since it's asking how wide the river could be?

edit: SOrry I don't really understand what I'm even supposed to draw in the diagrams of the components

Solving for the 't' would get the 'd'.

Draw the 30m/s at an angle θ and split it into vertical and horizontal components.
 
  • #5
Can I get something step by step please? I drew the components but I don't get why I even have to have both an x and the y. I just have two sets of axes and a theta angle at 90degrees
 
  • #6
stressedgirl said:
Can I get something step by step please? I drew the components but I don't get why I even have to have both an x and the y. I just have two sets of axes and a theta angle at 90degrees

You will see why you need it soon.

Did you get your components as

y: 30sinθ

x: 30 cosθ

These are your initial velocity components

Now consider vertical motion: y=vyt-0.5gt2

When the ball hits the other side of the river, y = 0. So solve for 't' and tell me what you get.
 

FAQ: Calculating Maximum River Crossing Distance with Initial Velocity of 30 m/s

What is 2-d kinematics?

2-d kinematics is a branch of physics that deals with the motion of objects in two dimensions. It involves analyzing the position, velocity, and acceleration of objects as they move in a two-dimensional plane.

What are the key variables in a 2-d kinematics problem?

The key variables in a 2-d kinematics problem are position (x and y), velocity (vx and vy), acceleration (ax and ay), and time (t). These variables are used to describe the motion of an object in two dimensions.

How is 2-d kinematics different from 1-d kinematics?

In 2-d kinematics, the motion of an object is described in two dimensions (x and y), while in 1-d kinematics, the motion is only described in one dimension (usually x). This means that in 2-d kinematics, there are two sets of equations for position, velocity, and acceleration, while in 1-d kinematics, there is only one set of equations.

What is the difference between displacement and distance in 2-d kinematics?

Displacement is a vector quantity that represents the change in position from an initial point to a final point, while distance is a scalar quantity that represents the total length of the path traveled by an object. In 2-d kinematics, displacement takes into account both the change in x and y position, while distance only considers the total distance traveled.

How can vectors be used in 2-d kinematics?

Vectors can be used in 2-d kinematics to represent the direction and magnitude of an object's position, velocity, and acceleration. They are often used to break down motion in two dimensions into horizontal and vertical components, making it easier to solve problems involving angles and direction.

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