Velocity vector and Max Height

In summary, the question asks whether a fly ball, with a velocity of v->=25i-4.9j, has passed its highest point. The answer in the book states that it has not, but the poster believes it has based on the downward motion indicated by the -4.9j component. The poster questions whether they are incorrect or if the book is wrong.
  • #1
ProRip
1
0
This is a question from "Fundamentals of Physics 8th Edition Extended, Chapter 4, Checkpoint3."

"At a certain instant, a fly ball has velocity v->=25i-4.9j (the x-axis is horizontal, the y-axis is upward, and the v-> is in metres per second). Has the ball passed its highest point?

The answer in the book says it hasn't...?

But I believe it has as -4.9j means the ball is now falling towards the ground therefore it has past its max height within the projectile motion.

Am I incorrect, or is the book wrong??, If I'm incorrect can someone point out why?
 
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  • #2
Welcome to PF!

Hi ProRip ! Welcome to PF! :smile:
ProRip said:
"At a certain instant, a fly ball has velocity v->=25i-4.9j (the x-axis is horizontal, the y-axis is upward, and the v-> is in metres per second). Has the ball passed its highest point?

The answer in the book says it hasn't...?

But I believe it has as -4.9j means the ball is now falling towards the ground therefore it has past its max height within the projectile motion.

Yup … minus j means it's moving downward …

looks as if the book is wrong! :redface:
 
  • #3


I cannot definitively say whether the book is wrong or not without further information. However, based on the given velocity vector, it does seem that the ball has passed its maximum height. The vector component -4.9j indicates that the ball is moving downward in the y-direction, which would suggest that it has reached its peak height and is now falling. It is possible that there is a mistake in the book or that the question is not worded correctly. It would be helpful to have more context or information to accurately determine the answer. Additionally, it would be beneficial to double check the calculations and equations used to solve the problem to ensure accuracy. Overall, it is always important to critically evaluate and question information, even from reliable sources, in order to fully understand and learn about a topic.
 

What is a velocity vector?

A velocity vector is a mathematical representation of an object's velocity, which includes both its speed and direction. It is typically represented as an arrow, with the length and direction of the arrow indicating the magnitude and direction of the velocity, respectively.

What is the formula for calculating velocity vector?

The formula for calculating velocity vector is:
v = d/t
Where v is the velocity vector, d is the displacement or distance traveled, and t is the time taken to travel that distance.

How is velocity vector related to acceleration?

Velocity vector and acceleration are related because acceleration is the rate of change of an object's velocity. This means that any changes in velocity, whether it is an increase or decrease in speed or a change in direction, will result in acceleration. In other words, acceleration is the derivative of velocity.

What is the maximum height of an object thrown vertically?

The maximum height of an object thrown vertically depends on the initial velocity, the acceleration due to gravity, and the time it takes to reach its peak. The formula for calculating maximum height is:
h = (v2sin2θ)/2g
Where h is the maximum height, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

How does air resistance affect the velocity vector and maximum height of an object?

Air resistance, also known as drag, opposes the motion of an object and can decrease its velocity. This means that an object with air resistance will have a lower velocity vector and a shorter maximum height compared to an object without air resistance. The amount of air resistance depends on factors such as the shape, size, and speed of the object.

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