Respuesta :
Answer:
Second projectile is 1.4 times faster than first projectile.
Explanation:
By linear momentum conservation
Pi = Pf
m x U + M x 0 = (m + M) x V
[tex]U= \dfrac{(m + M)\times V}{m}[/tex]
Now Since this projectile + pendulum system rises to height 'h', So using energy conservation:
KEi + PEi = KEf + PEf
PEi = 0, at reference point
KEf = 0, Speed of system zero at height 'h'
[tex]KEi = \dfrac{(m + M)\times V^2}{2}[/tex]
PEf = (m + M) g h
So,
[tex]\dfrac{(m + M)\times V^2}{2} + 0 = 0+ (m + M) g h[/tex]
[tex]V =\sqrt {2gh}[/tex]
So from above value of V
Initial velocity of projectile =U
[tex]U=\dfrac{(M+m)\sqrt{2gh}}{m}[/tex]
Now Since mass of projectile and pendulum are constant, So Initial velocity of projectile is proportional to the square root of height swung by pendulum.
Which means
[tex]\dfrac{U_2}{U_1}=\sqrt{\dfrac{h_2}{h_1}}[/tex]
[tex]U_2=\sqrt{\dfrac{h_2}{h_1}}\times U_1[/tex]
[tex]U_2=\sqrt{\dfrac{5.2}{2.6}}\times U_1[/tex]
U₂ = 1.41 U₁
Therefore we can say that ,Second projectile is 1.4 times faster than first projectile.
