ABC is an equilateral triangle in a vertical plane. from point A a projectile is projected suchi that it just grazes B and lands at C. the angle of projection x is
Answers
Given : ABC is an equilateral triangle in a vertical plane. From point A a projectile is projected such that it just grazes Band lands at C.
To Find : The angle of projection
Solution:
Assume that length of Equilateral triangle = 2x ( AB = BC = AC = 2x)
Then Height of Triangle = √((2x)² - x²) = √3x
Let say after 2T time it reaches C then time T to reach mid way at point B.
Projected with speed V at angle α
VCosα * 2T = 2x
=> VCosα * T = x
=> VCosα = x/T
=> x = VCosα.T
for vertical
S = √3x
t = (2T/2) = T
a = -g
Velocity at top = 0
V = u + at
0 = VSinα - gT
=> VSinα = gT
S = ut + (1/2)at²
√3x = VSinα * T + (1/2)(-g)T²
=> √3x = VSinα * T - (1/2)(gT).T
Substitute gT = VSinα , x = VCosα.T
=> √3VCosα.T = VSinα * T - (1/2)VSinαT
cancel VT
=> √3Cosα = Sinα - (1/2)Sinα
=> √3Cosα = (1/2)Sinα
=> 2√3 = Sinα/Cosα
=> tanα = 2√3
=> α = tan⁻¹(2√3)
=> α = 73.9°
The angle of projection is 73.9°
Learn More:
3. A body is projected horizontally with a speed v. Find the velocity of ...
https://brainly.in/question/10682846
From the top of a tower of height 78.4 m two stones are projected ...
https://brainly.in/question/20322930
hope it's helpful for u dear ❤️
