Need help solving A and B Items Constants Y Part A A 26 g rifle bullet traveling

Question

Need help solving A and B

Items Constants Y Part A A 26 g rifle bullet traveling 220 m/s embeds itself in a 3.4-kg pendulum hanging on a 2.7-m-long string, which makes the pendulum swing upward in an arc. (Figure 1) C Thi Determine the vertical component of the pendulum's maximum displacement Express your answer to two significant figures and include the appropriate units. 2. A B Figure 1 of 1 3. Mon Aax Value Units 4. Th Submit Part B 6. The Determine the horizontal component of the pendulum's maximum displacement. Express your answer to two significant figures and include the appropriate units. 7. Pro 772 9. Pro Armax :1 Vahle Units

Explanation / Answer

A) let

m = 26 g = 0.026 kg, v = 220 m/s

M = 3.4 kg

L = 2.7 m

let v' is the velocity of pendulum and bullet just after the bullet embeded into the pendulum.

Apply conservation of momentum

m*v = (m + M)*v'

==> v' = m*v/(m + M)

= 0.026*220/(0.026 + 3.4)

  
= 1.67 m/s

delta_ymax = v'^2/(2*g)

= 1.67^2/(2*9.8)

= 0.142 m <<<<<<<-------------------Answer

B) let theta is the angle made by the thread with vertical.

delta_ymax = L*(1 - cos(theta))

0.142 = 2.7*(1 - cos(theta))

0.142/2.7 = 1 - cos(theta)

cos(theta) = 1 - 0.142/2.7

theta = cos^-1(0.9474)

= 18.7 degrees

delta_xmax = L*sin(theta)

= 2.7*sin(18.7)

= 0.866 m <<<<<<<-------------------Answer

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