What is the initial speed v0 of the ball?

In summary, the initial speed v0 of the ball is determined by solving for it in the equation v0^2 = v^2 + 2gh - gh0. The height of the ball when the vertical speed is 1/2 of the initial speed vo is given by the equation h = 1/2 (3/4 vo2)/g + ho. When solving for the initial speed, it is important to consider the 1/2 and 2 in front of the v2 terms.
  • #1
Spruance
33
0
energifigur.gif


1) What is the initial speed v0 of the ball?

2)What is the height of the ball when the vertical speed is 1/2 of the initial speed vo?

Thanks
(I'm so sorry for my bad english. It's not my mother tongue)
 
Last edited:
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  • #2
Well, vo is the magnitude of the velocity, and since velocity is a vector, there must be a unit vector associated with that magnitude, however . . .

one must determine the vertical displacement after the ball is deflected up, and actually, I believe the appropriate question is "what is the height of the ball when the vertical speed is 1/2 of the initial speed vo?"

One could use conservation of energy.
 
Last edited:
  • #3
We have:

0.5mv^2+mgh = 0.5mv0^2+mgh0

v0^2 = -2mgh0 + mv^2 + 2mgh

v0 = (-2gh0 + v^2 + 2gh)^1/2

v0 = (- 2 * 9.81 * 4 + o m/s + 2 * 9.81 * 3)^1/2

v0 = (- 78 + 58.86)^1/2

Here is something wrong
 
  • #4
The initial equation 0.5mv^2+mgh = 0.5mv0^2+mgh0 is incorrect.

One is solving for the h, when v = vo/2, so

0.5 m (vo/2)2 + mgh = 0.5 m vo2 + mgho and m divides out, so

0.5 (vo/2)2 + gh = 0.5 vo2 + gho, and the re-arrange terms to get

h = ho + 1/g ( . . . )
 
  • #5
Hi, thanks

Maybe I must edit my first question.

What I meant was:

1) How fast must the initial speed v0 be, if the ball shall reach 4 meters into the air (at the heighest, of course)
 
  • #6
Hi

I tried to rearrange your equation:

0.5 (vo/2)2 + gh = 0.5 vo2 + gho

I get:

h = ((v0^2)-(v0^8)+gh0))/(g)

Maybe I am just stupid
 
  • #7
In h = ((v0^2)-(v0^8)+gh0))/(g), the kinetic energy terms should be

vo2 - (vo/2)2 =

vo2 - vo2/4 = 3/4 vo2

and let's not forget the 1/2 in front of the v2 terms,

so the equation for h should be

h = 1/2 (3/4 vo2)/g + ho =

3/8 (vo2)/g + ho
 
  • #8
To solve for the initial speed v0:

v0^2 = v^2 + 2gh - gh0

v0 = (v^2 + 2gh - gh0)^1/2

v0 = (2g(h-h0))^1/2

v0 = (2 * 9.81 (4 m -3 m))^1/2

v0 = 4.43 m/s

What is wrong?
 
  • #9
Spruance said:
To solve for the initial speed v0:

v0^2 = v^2 + 2gh - gh0

v0 = (v^2 + 2gh - gh0)^1/2

v0 = (2g(h-h0))^1/2

v0 = (2 * 9.81 (4 m -3 m))^1/2

v0 = 4.43 m/s

What is wrong?
you forgot a 2 in the first equation but then you put it back later so the answer should be right. How do you know it's not? (if you are using Webassign, it may be simply a question of sig figs)
 
  • #10
Ok.

Let us assume that the initial speed is 4.43 m/s

then the height of ball is given:

h = 1/2 (3/4 vo2)/g + ho =

3/8 (vo2)/g + ho

= 3/8 * ((4.43^2)/9.81) + 3

= 3.75 m

Is that correct?
 
  • #11
Spruance said:
Ok.

Let us assume that the initial speed is 4.43 m/s

then the height of ball is given:

h = 1/2 (3/4 vo2)/g + ho =

3/8 (vo2)/g + ho

= 3/8 * ((4.43^2)/9.81) + 3

= 3.75 m

Is that correct?
you shoudl have mentioned that you has switched to question 2 now...
Yes, that looks right.
 

1. What is the definition of initial speed?

Initial speed, also known as the initial velocity, is the rate at which an object moves in a specific direction at the beginning of its motion. It is typically measured in units of meters per second (m/s).

2. How is initial speed different from final speed?

The initial speed refers to the velocity of an object at the start of its motion, while the final speed is the velocity at the end of its motion. The initial speed can be different from the final speed if the object accelerates or decelerates during its motion.

3. What factors affect the initial speed of a ball?

The initial speed of a ball can be affected by several factors, including the force applied to the ball, the angle at which it is thrown or launched, the mass of the ball, and the air resistance or drag on the ball.

4. How is initial speed calculated?

The initial speed can be calculated using the formula v0 = (s/t), where v0 is the initial speed, s is the distance the object travels, and t is the time it takes to travel that distance. Alternatively, if the initial and final speeds are known, the initial speed can be calculated using the formula v0 = (v + vf)/2, where v is the initial speed and vf is the final speed.

5. Why is it important to know the initial speed of a ball?

Knowing the initial speed of a ball is important in understanding and predicting its motion. It can help determine the trajectory of the ball, how far it will travel, and how fast it will move. This information is valuable in various fields such as sports, engineering, and physics.

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