A projectile is launched from ground level with speed u at an angle

of above the horizontal.
Find in terms of u,

o

and g by proving:

I. the maximum height H attained by the projectile,

II. the distance from the starting point at which the

projectile strikes the ground; this is called the range R

of the projectile.

III. The total time of flight

I. H = U² Sin²θ/2g

II. R = U² Sin 2θ/g

III. T = 2U Sinθ/g

Explanation:

We have a projectile motion with:

U = launch speed of projectile

θ = Angle of launch speed with horizontal surface

Ux = U Sinθ = Horizontal Component of Launch Speed

Uy = U Sinθ = Vertical Component of Launch Speed

H = Maximum Height attained by Projectile

R = Range of Projectile

t = Time to reach maximum height

T = 2t = Total Time of flight

I.

For H:

Considering the vertical motion of projectile, we use 3rd eqn. of motion:

2gh = Vf² - Vi²

here,

Vf = 0 m/s   (Because projectile stops at highest point)

Vi = Uy = U Sinθ

g = -g  (For upward motion)

h = H

Therefore,

-2gH = 0² - (U Sinθ)²

H = U² Sin²θ/2g

III.

For T:

Considering the vertical motion of projectile, we use 1st eqn. of motion:

Vf = Vi + gt

here,

Vf = 0 m/s   (Because projectile stops at highest point)

Vi = Uy = U Sinθ

g = -g  (For upward motion)

Therefore,

0 = U Sinθ - gt

t = U Sinθ/g

Therefore,

T = 2t

T = 2U Sinθ/g

II.

For R:

We neglect air resistance in our analysis, sue to which the horizontal velocity of projectile remains constant. Therefore:

S =Vt

where,

S = R

V = Ux = U Cosθ

t = T = 2U Sinθ/g

Therefore,

R = (U Cosθ)(2U Sinθ/g)

R = U²(2 SinθCosθ)/g

Since, Sin 2θ = 2 SinθCosθ

Therefore,

R = U² Sin 2θ/g

a high pressure system is a dense air mass that is usually cooler and drier than the surrounding air. a low pressure system is a less dense air mass that is usually wetter and warmer than the surrounding air.

in general, areas that experience high atmospheric pressure also experience fair weather. low pressure systems can cause the formation of clouds and storms. air usually flows from areas of high pressure to areas of low pressure..

heat the gas and measure the pressure