Question

Show that projectile follow a parabolic path and also derive an expression for maximum height attained and total oil until range cover by the project project tiles

Answer 1

let assume the ball is thrown into the space with velocity V at some angle Ɵ with respect to horizontal .
horizontal (x axis ) components
Vx = VcosƟ
a = gcos90° = 0
displacement = Range = R
time taken = T

vertical (y axis ) components
Vy = VsinƟ
a = -gsin90° = -g
displacement in y direction when ball reaches the ground = 0 .
time taken = T

S = UyT + ayT²/2
0 = (2Uy+ayT)T
0 = 2VsinƟ - gT
-2VsinƟ = - gT
T = 2VsinƟ/g

at Max height vertical final velocity = Vf = 0
Vf² - Vy² = 2aS
0² - (VsinƟ)² = -2gH
-V²sin²Ɵ = - 2gH
H = V²sin²Ɵ/2g

Final horizontal speed is always remain constant because there is no acceleration (if air resistance is neglected)
V = S/T
S = VT
R = VcosƟ × 2VsinƟ/g
R = V²2sinƟcosƟ/g
R = V²sin2Ɵ/g