Answer:
313.8 m/s
Explanation:
Momentum p must be conserved.
The momentum before the collision:
![p=m_{bullet}v_{bullet} + m_{block}v_{block}](https://tex.z-dn.net/?f=p%3Dm_%7Bbullet%7Dv_%7Bbullet%7D%20%2B%20m_%7Bblock%7Dv_%7Bblock%7D)
The momentum after the collision:
![p=(m_{bullet}+m_{block})v_{bullet+block}](https://tex.z-dn.net/?f=p%3D%28m_%7Bbullet%7D%2Bm_%7Bblock%7D%29v_%7Bbullet%2Bblock%7D)
Solving both equations:
![v_{bullet}=\frac{(m_{bullet}+m_{block})v_{bullet+block}}{m_{bullet}}](https://tex.z-dn.net/?f=v_%7Bbullet%7D%3D%5Cfrac%7B%28m_%7Bbullet%7D%2Bm_%7Bblock%7D%29v_%7Bbullet%2Bblock%7D%7D%7Bm_%7Bbullet%7D%7D)
Answer:
The distance is, y = 489.5 [m/s]
Explanation:
To solve this problem we can use the following equation of kinematics.
![v_{f}^{2}= v_{i}^{2}+(2*g*y)](https://tex.z-dn.net/?f=v_%7Bf%7D%5E%7B2%7D%3D%20%20v_%7Bi%7D%5E%7B2%7D%2B%282%2Ag%2Ay%29)
where:
Vf = final velocity = 98 [m/s]
Vi = initial velocity = 0
g = gravity acceleration = 9.81 [m/s^2]
y = distance [m]
(98^2) = 0 + (2*9.81*y)
Note: the positive sign of the equation means that the acceleration of gravity acts in the direction of the movement of the object.
9604 = 19.62*y
y = 489.5 [m/s]