A projectile of mass M explodes at thee
highst point of its trajectory when it hase
vlocity . The horizontal distance travelede
btween launch and explosion is x_0 . Two
fragments are produced with initiale
velocitis parallel to the ground. They
thenfollow their trajectories until they hitt
he ground. The fragment of mass m_1 retuns exactly to the launch point of thei
orginal projectile (of mass M) while thee
othr fragment of mass m_2 hits the grounda
t a distance D from this point. Disregardn
iteraction with air and assume that massa
ws conserved in the explosion (m_1 +m_2 =M) Determine the magnitude of the
velocity of fragment 2 just before it hits theground.
(a) ((gx_0 )/v)
(b)(√((25)/9))v
(c) (√(((25)/9)v^2 +(((gx_0 )/5))2))
(d)(√((5/3)x_0 v^2 +(((gx_0 )/v))2))
If , 0 ⇢ M′ ⇢^f M⇢^g M′′⇢0 is
a short exact sequence and M′ , M′′ are
two finitely generated R −modules
then prove M is finitely generated.
Hint: f , g are two R − homomorphism.