Section-D
la) A stone is projected, from the ground, with a velocity u, at an angle
0 with the horizontal. Show that it describes a parabolic path and
hence obtain expression for the maximum height attained.
Answers
Answer:
Explanation:
A projectile is fired with a velocity u, making an angle θ with the horizontal. Show that its trajectory is a parabola and find out its time of flight , maximum height attained and horizontal range.
Consider the following equations of a projectile with angle
of projection θ and initial velocity v
0
- here
x=v
ox
t refer to book ;
rearrange the expression for time t ,
t=
v
0x
x
substituted
v
ox
x
for in the expression
y=(v
0
sinθ)t−
2
1
gt
2
y=v
oy
(
v
ox
x
)−
2
1
g(
v
0x
x
)
2
substitute v
o
cosθ for v
ox
sin θ for v
oy
in the above expression.
Y=(v
0
sinθ)(
v
o
cosθ
x
)−
2
1
g(
v
o
cosθ
x
)
2
Hence the obtained equation of the projectile is
Y=(tanθ)x−(
2(v
o
)
2
gsec
2
θ
)x
2
The expression is to be obtained in the form of
Y = ax+bx
2
.
hence it is a parabolic motion so from it we get all the required quantities