Answer:
33.14 m/s
Explanation:
The mass of the block is 121g or .121 kg. As the bullet is lodged in the block the total mass is 121+14 = 135 g or 0.135 kg.
The frictional force that makes the block come to a stop is normal force* coefficient of friction = 0.135 * 9.8 * 0.7 = 0.9261 N
As the block comes to rest after sliding for 8.3 meters the energy it was given by the bullet is
0.135 * 9.8 * 0.7 * 8.3
= 7.69 Nm
Now this energy is provided the bullet. So the energy in the bullet was equal to
1/2 * mv² = 0.5 * 14 * v².
0.5 * 0.014 * v^2 = 0.135 * 9.8 * 0.7 * 8.3 = 7.69
=> 0.007 * v² = 7.69
=> v² = 7.69 / 0.007
=> v² = 1098.57
=> v = √1098.57
=> v = 33.14 m/s
Humans,trees,plants hope it helps
Your book has applied the chain rule to produce:
dv/dt = dv/dx * dx/dt
Now, we can get dv/dx by:
1) Differentiate
x = vt, with respect to v.
dx/dv = t
Now, if we take the inverse of this, we can obtain dv/dx
dv/dx = 1/t
This is also proven by the fact that dv/dx is the change in velocity and if you multiply it by dv/dx, which is equivalent to dividing by the change in time, as we just proved, then you obtain acceleration.
Newton's law applies here because an object in motion (your body) stays the speed that you were going, so if you were hit, your body would keep going when the car is stopped. This causes your body (especially your neck) to whip back and possible break.