A projectile is thrown at angle 30 degree with surface of earth with velocity v such it attain maximum height equal to radius of earth
Answers
Answer:
Explanation:
Let us consider a ball projected at an angle θ with respect to horizontal x-axis with the initial velocity u .
The point O is called the point of projection, θ is the angle of projection and OB = horizontal range. The total time taken by the particle from reaching O to B is called the time of flight.
Now,
(a). The total time of flight is
Resultant displacement is zero in Vertical direction.
Therefore, by using equation of motion
s=ut−
2
1
gt
2
gt=2sinθ
t=
g
2sinθ
(b). The horizontal range is
Horizontal range OA = horizontal component of velocity × total flight time
R=ucosθ×
g
2usinθ
R=
g
u
2
sin2θ
(c). The maximum height is
It is the highest point of the trajectory point A. When the ball is at point A, the vertical component of the velocity will be zero.
By using equation of motion
v
2
=u
2
−2as
0=u
2
sin
2
θ−2gH
H=
2g
u
2
sin
2
θ
Hence, this is the required solution