A spherical non-rotating planet (with no atmosphere) has mass m
1= 6
×10
24 kg and radius
r
1= 9000
km. A projectile of mass m
2≪
m
1 is fired from the surface of the planet at a point
A with a speed
v
A at
an angle α=30
∘ with respect to the radial direction. In its subsequent trajectory the projectile reaches a
maximum altitude at point B on the sketch. The distance from the center of the planet to the point
B is
r
2=(5/2)
r
1. Use
G=6.674×10
−11 k
g
−1
m
3
s
−2.
What is the initial speed v
A of the projectile? (in m/s)
v
A=