The only way to get the height the profressor has is to get the radical of (v^2)

Question

The only way to get the height the profressor has is to get the radical of (v^2)/(2*g) and im not sure that formula is right.

A bullet with a mass of 4 g is fired at a speed of 600 m/s into a ballistic pendulum of mass of 1 kg and a thickness of 25 cm. The bullet passes through the pendulum and emerges with a speed of 100 m/s. Calculate the constant retarding force acting on the bullet in its passage through the block, (b) the height to which the pendulum rises and (c) the time it took to rise. (a 2792 b- 45 4) block, (b) the height to which the pendulum rises and (c) the time it took to rise. (a 2792 b-45 c- 72 ms)

Explanation / Answer

a)initial velocity of bullet = u=600m/s

velocity after bullet emerges from pendulum = v=100m/s

Distance travelled to decelerate = thickness of pendulum =s= 25cm = 0.25m

v2=u2+2as

1002=6002+2*a*0.25

deceleration=a=700000m/s2

retarding force =F=ma = 0.004*700000=2800N

b)Initial momentum of system = mbulletvbullet = 0.004*600 = 2.4kg-m/s

Final momentum of system = mbulletvbullet + mpendulumvpendulum

= (0.004*100)+(1*vpendulum)

From conservation of momentum, 2.4 = 0.4+vpendulum

vpendulum = 2m/s

Let us apply conservation of energy in the pendulum.

Let h be maximum height reached by pendulum

(1/2)mpendulumvpendulum2 = mpendulumgh

h = vpendulum2 /2g = 22/(2*9.8) = 0.204m

c) h=(1/2)gt2

t = sqrt(2h/g) = 0.204second

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