The particle now moves along the tangent PT in a free para bolic path, its initial velocity being 8 ft./sec. inclined at an angle Cos 1 3 to the horizon. Vertical component of initial velocity=8 sin 8 -3√5 ft./sec.
A tax is a compulsory payment by the subjects of a state. It is levied, not for the benefit of individuals, but for the benefit of people at large. A tax lins four main characteristics

1. It is a compulsory payment. The taxpayer has no choice but to pay it. No one can refuse to pay the tax on the ground that he is not being benefited by the services. rendered by the government. Since in a trajectory, at the highest point, the direction of velocity is along the horizontal, the vertical component of the velo city at the highest point is zero. .. if h is the greatest height reached by the particle, then burden of tax will be equal on buyers and sellers i.e., price will 1 rise by of amount of tax. Amount of tax is 2 AC. As a result of tax, price of commodity has increased from PM to AN i.e., by AB which is 1 2 of AC i.e. AB=BC. Thus half of tax burden by more AB=of AC) is on the buyers and other half of tax burden shouldered by the sellers. 0-( √5)²-2gh.

2. Being a compulsory payment, it involve some sacrifice to the taxpayer.

3. It is meant to defray general expe incurred by the state for the benefit of general public, not any particular typ expenses. In India huge amount is being on the welfare and uplift of the back classes. This expenditure does not benef A backward classes only, but it is for the t of the society as a whole.

4. There is no direct 'quid-pro-quo] bet the amount of the tax paid and the bea received. In other words, an individual pa a certain amount of tax cannot claim an benefit in return. As Prof. Taussing tax The essence of a tax, as distinguished other charges by the government, is t absence of a direct quid-pro-quo between taxpayer and the public authority" h=/ft. Ex. 2. Show that the greatest angle through which a person can oscillate on a swing, the Fopes of which can support twice the person's weight when at rest is 120°. If the ropes are strong enough and he can swing through 180° and if v is his speed at any point, prove that the tension in the ropat that point is3my21 length of the rope. where m is the mass of the person.

Let u be the initial velocity and be the velocity in the position P when the ropes are inclined at an angle 8 to the vertical. Then y²²-2g/(1-cos 8)

The equation of motion along the normal at P is=T-mg cos 8 -m[8 +门 T-mg cos + 8 cos 0+-28 (1-cos) or =m[4-28+38 cos 9 ] TIM T-2mg and 6-0 in (2), we get Putting

However, it should not be concluded fra the above that only those persons are entice to public services who pay taxes. Every entitled to public services and in fact th people who do not pay taxes or pay little g more public services because they belong t the poor section of the community.

Question: 

1. If a body moves so that the feet which it moves in t seconds is given by the relation s=at³, find the velocity and the acceleration. Find the velocity and acceleration after 2 seconds?