Question

A gun is fired it, as shown in the f 6. 1 kok fwat rst on a thin horiontal sheet direcely aboe vertically into a m figure below If the bullet has a mass of 21.4 g and a speed of t- 300 m/s, how high will the block rise into the air after the bullet becomes embedded in it? 7. An 19.8 g rifle bullet traveling 221 m/s buries itself in a 3.76 kg pendulum hanging on a 2.84 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's displacement

Answer 1

6.

m=1.38kg, M=0.0214kg, v=300m/s, v_1i=0m/s

Use law of conservation of linear momentum

P_f=P_f

m₁v_1i +m₂v_2i = m₁v_1f +m₂v_2f

m_*v_1i +M*v = (m₁+m₂)*v_common

1.38*0+0.0214*300 = (1.38+0.0214)*v_common

v_common= 4.58m/s

This is initial velocity of block+bullet in vertical direction

Thus v_i=v_common= 4.58m/s

At max height v_f=0m/s

Use kinematic eqn in vertical direction

v_f²= v_i² -2gh_max

Plugging values,

0^2=4.58^2-2*9.8*h_max

h_max=1.07m

4.58m/s