Finding the acceleration vector component

In summary, the problem is to find the acceleration component of a vertically upward traveling ball with quadratic air resistance. The relevant equations are: F=ma, W=-mgi, R=-C^2D^2V^2, and a(t)=dv/dt. After attempting to integrate, the result does not make sense. However, the problem actually asks for the acceleration, not the velocity. The correct equation for the acceleration is r(t)=-g-(C*D^2*v/m), and differentiating this twice should provide the correct answer.
  • #1
jimmy42
51
0

Homework Statement



A ball travels vertically upward with quadratic air resistance, find the acceleration component.

Homework Equations



So, I have x pointing vertically downward and

C=0.20 D = Diameter V=velocity

W= -mgi
R = -C^2D^2V^2

F=ma

ma= -mg-C^2D^2V^2


The Attempt at a Solution




a(t)= dv/dt

dv/dt = (-mg-C^2D^2V^2)/m


After doing the integration it seems not to make any sense. Any help where I have gone wrong? Am I along the right lines?
 
Physics news on Phys.org
  • #2
Well, why are you integrating? The problem, according to you, asks for the acceleration, not the velocity.
 
  • #3
OK, I think that just got me the equation for the acceleration of a resisted projectile

r(t)= -g - (c*D^2*v/m)

So, differentiating this twice should give the acceleration componet? I know the answer I should get and it does not match. Any help?
 

FAQ: Finding the acceleration vector component

What is the acceleration vector component?

The acceleration vector component refers to the measure of acceleration in a specific direction or axis. It is a vector quantity that includes both magnitude and direction.

How is the acceleration vector component calculated?

The acceleration vector component can be calculated by dividing the total acceleration by the cosine of the angle between the direction of motion and the chosen axis. The formula for finding the acceleration vector component is: ax = a cos θ, where ax is the acceleration component in the x-axis, a is the total acceleration, and θ is the angle between the direction of motion and the x-axis.

What is the difference between acceleration and acceleration vector component?

Acceleration is a scalar quantity that measures the rate of change of velocity, while acceleration vector component is a vector quantity that measures the rate of change of velocity in a specific direction or axis. Acceleration includes only magnitude, while acceleration vector component includes both magnitude and direction.

What are some real-world applications of finding acceleration vector component?

Finding the acceleration vector component is important in many fields such as physics, engineering, and sports. It is used to calculate the acceleration of objects in motion, design structures that can withstand certain accelerations, and analyze the performance of athletes in different sports.

Can the acceleration vector component be negative?

Yes, the acceleration vector component can be negative. This indicates that the acceleration is in the opposite direction of the chosen axis. For example, if the chosen axis is the x-axis and the acceleration vector component is -5 m/s2, this means that the object is accelerating at a rate of 5 m/s2 in the negative direction of the x-axis.

Similar threads

Find v(t) from Newton's Second Law and Differential Equation
Replies
3
Views
1K
Differential equation for the acceleration of an oscillating particle
Replies
9
Views
2K
Finding the flow of a vector field
Replies
5
Views
2K
Integrate Equation: Find Position with Initial Drag Force & Velocity
Replies
13
Views
2K
What are the components of u-w?
Replies
2
Views
1K
Find time elapsed, given Force as a function f(velocity,displacment)
Replies
2
Views
2K
Find its velocity as a function of time?
Replies
2
Views
2K
Atwood's with a cylinder - Rotational Motion
Replies
12
Views
254
How to find tangential and normal acceleration?
Replies
1
Views
2K
Simple projectile motion question
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top