Answer:
x = 0.54 m
y = 0.058 m
Explanation:
m = mass of the bullet = 16 g = 0.016 kg
v = speed of bullet before collision = 240 m/s
M = mass of the pendulum = 3.6 kg
L = length of the string = 2.5 m
h = height gained by the pendulum after collision
V = speed of the bullet and pendulum combination
Using conservation of momentum
m v = (m + M) V
(0.016) (240) = (0.016 + 3.6) V
V = 1.062 m/s
Using conservation of energy
Potential energy gained by bullet and pendulum combination = Kinetic energy of bullet and pendulum combination
(m + M) g h = (0.5) (m + M) V²
(9.8) h = (0.5) (1.062)²
h = 0.058 m
y = vertical displacement = h = 0.058 m
x = horizontal displacement
horizontal displacement is given as
x = sqrt(L² - (L - h)²)
x = sqrt(2.5² - (2.5 - 0.058)²)
x = 0.54 m
