Simple kinematics problem I can't figure out

In summary, a ball is thrown down with an initial velocity of 2.0 m/s from a height of 1.75 m. It takes 0.36 seconds for it to hit the ground.
  • #1
MRi04
6
1

Homework Statement


A ball is thrown down with an initial velocity of 2.0 m/s from a height of 1.75 m, determine how long until it hits the ground.

initial velocity = 2 m/s
distance = 1.75 m
acceleration = 9.8 m/s2
time = ?

Homework Equations


d=vit+1/2a(t)2

The Attempt at a Solution


1.75=2t + 1/2(9.8)t2
1.75=2t + 4.9t2
Square root of both sides?
1.32 = 1.4t + 2.21t
1.32 = 3.61t
All divided by 3.61?
t = 0.36
... I know the solution to be 0.43 seconds, but can't get there!

Any help is greatly appreciated!
 
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  • #2
MRi04 said:

Homework Statement


A ball is thrown down with an initial velocity of 2.0 m/s from a height of 1.75 m, determine how long until it hits the ground.

initial velocity = 2 m/s
distance = 1.75 m
acceleration = 9.8 m/s2
time = ?

Homework Equations


d=vit+1/2a(t)2

The Attempt at a Solution


1.75=2t + 1/2(9.8)t2
1.75=2t + 4.9t2
Square root of both sides?
That is where you went wrong...
Solve this as a quadratic equation.
 
  • #3
MRi04 said:

Homework Statement


A ball is thrown down with an initial velocity of 2.0 m/s from a height of 1.75 m, determine how long until it hits the ground.

initial velocity = 2 m/s
distance = 1.75 m
acceleration = 9.8 m/s2
time = ?

Homework Equations


d=vit+1/2a(t)2

The Attempt at a Solution


1.75=2t + 1/2(9.8)t2
1.75=2t + 4.9t2
Square root of both sides?
1.32 = 1.4t + 2.21t
1.32 = 3.61t
All divided by 3.61?
t = 0.36
... I know the solution to be 0.43 seconds, but can't get there!

Any help is greatly appreciated!
In your solution,you took square root of both sides which is incorrect.Instead,solve the quadratic equation formed in t.You will get the time taken.
 
  • #4
Thanks RUber and Ellispson, really appreciate it, can you give any more detail, I'm not sure how to do that?
 
  • #5
If you have an equation of the form : At^2 + Bt + C = 0, then
##t = \frac{ -B \pm \sqrt{B^2 - 4AC}}{2A}##
Only one of the solutions will be a positive time...choose that one.
 
  • #6
RUber said:
If you have an equation of the form : At^2 + Bt + C = 0, then
##t = \frac{ -B \pm \sqrt{B^2 - 4AC}}{2A}##
Only one of the solutions will be a positive time...choose that one.

but what does C represent in the quadratic equation? Sorry, it has been a long time since I have used the quadratic equation.
 
  • #7
MRi04 said:
but what does C represent in the quadratic equation? Sorry, it has been a long time since I have used the quadratic equation.
I mean, what does it represent in terms of the problem I posted?
 
  • #8
You have 1.75 = 2t + 4.9t^2 . Can you put that into the form of At^2 + Bt + C = 0? C is the number that is not multiplied by t or t^2...I get -1.75.
 
  • #9
MRi04 said:
I mean, what does it represent in terms of the problem I posted?
The constant term.Which means the term not having the variable t in it.
 
  • #10
RUber said:
You have 1.75 = 2t + 4.9t^2 . Can you put that into the form of At^2 + Bt + C = 0? C is the number that is not multiplied by t or t^2...I get -1.75.
Oh of course, I see. I'll try that now
 
  • #11
That worked for me! Thanks very much to both of you. Happy physics-ing!
 
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Likes Chestermiller

What is a simple kinematics problem?

A simple kinematics problem involves analyzing the motion of an object without considering the forces that cause the motion. It focuses on the position, velocity, and acceleration of the object.

Why can't I figure out this kinematics problem?

There can be a few reasons why you are having trouble solving a kinematics problem. It could be due to a lack of understanding of the concepts, incorrect use of equations, or missing information in the problem.

What are the steps to solving a simple kinematics problem?

The first step is to identify the known and unknown variables in the problem. Then, use the appropriate kinematics equations to solve for the unknown variable. It is important to pay attention to the units and use consistent units throughout the problem. Finally, check your answer for reasonableness.

Do I need to know calculus to solve kinematics problems?

No, you do not need to know calculus to solve simple kinematics problems. Basic algebra and understanding of the kinematics equations are sufficient.

How can I improve my skills in solving kinematics problems?

Practice is key in improving your skills in solving kinematics problems. Start with simple problems and gradually move on to more complex ones. It is also helpful to understand the underlying concepts and to regularly review and reinforce your understanding of kinematics.

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