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## Angle between velocity and acceleration

Discuss a circumstance in which angle between velocity and acceleration is less than 90.

Discuss a circumstance in which angle between velocity and acceleration lies batween 180 and 90.

(Hifsa Zafar asked this)

**Answer**:

In projectile motion when the object is moving up, the angle between velocity and acceleration (due to gravity g) is between 90 degree and 180 degree.

during the downward motion of a projectile, the angle between velocity and acceleration is between 0 and 90 degree.

## A Problem from Projectile motion

“A ball is projected vertically upwards with an initial velocity of 28m/s and is observed to pass a point 30m above the projection point,at what 2times does the ball pass these points?”

(Vimal Raj Answered)

ans : 1.356 sec and 1.444 sec .

sol:

from v=u+at we get t=2.8 . (time taken to reach the max height )

fm v^{2}-u^{2}=2aS we get S=39.2 m (max height reached)

observer at 30 m .

so , in btw distance btw observer and ball (at the top) =9.2 m

at top ball is at rest and time taken to reach the observer can be calculaed from S=ut + 1/2 at^{2} ,we get t=1.356s .

and next time can be calculated by 2.8 – 1.356 =1.444 sec .

**(The answer has not been scrutinized. If any error, teachers and visitors can post as comment)**

## Projectile motion on an inclined plane

Sourav asked:

“Can you tell me about projectile motion on an inclined plane?”

Answer:

Dear Sourav,

The question is already discussed in detail in the following sites. Please go through them. If you still have doubts, I can explain them in simpler terms.

- http://www.goiit.com/posts/list/mechanics-projectile-motion-in-inclined-plane-263.htm
- http://cnx.org/content/m14614/latest/

## Factors affecting frequency of sound produced by a stretched string

Smile asks:

Study how the frequency of sound produced will change in each case with the following strings of length 15cms when the strings are tied between 2 ends-

- aluminium string
- copper string
- cotton string
- metallic string
- jute string

Also study how the pitch changes when the strings are made taught and loose. Study how the frequency of sound changes with thickness of the following strings

- cotton strings
- copper strings

**Answer:**

*This seems to be a homework question or a project question. Therefore I am not giving a detailed answer so as not to tamper the basic aim of assigning a project.*

The frequency of sound produced by a stretched string depends on the following factors:

- the length of the string
- the linear mass density (i.e; the mass per unit length) of the string
- the tension in the string

When you are using strings of different materials, the factor which changes is the mass per unit length and the same is true when you are changing the thickness.

When you make the string more taut, the tension increases and vice versa.

The question is given for a constant length. Therefore the case of effect of changing length does not come into picture.

The formula showing the relationship is

it is evident from the formula that the frequency of sound is

- inversely proportional to the length
- directly proportional to the square root of tension in the string and
- inversely proportional to the square root of linear density of the string.
on proper substitution, the formula can be recast as

and this will be more convenient for you to answer the questions.

I recommend that you try to explore by actually performing the experiments.

Refer to http://www.tutorvista.com/content/physics/physics-iii/waves/stretched-strings-vibration.php for more