Final answer:
The resistive force exerted by the sand on the bullet is 2500 N, and the time taken for the bullet to come to rest is 0.002 seconds or 2 milliseconds.
Step-by-step explanation:
To calculate the resistive force exerted by the sand on the bullet as well as the time taken for the bullet to come to rest, we'll use the laws of motion and the work-energy theorem. The bullet has a mass (m) of 50g, which is 0.05 kg, and an initial velocity (v) of 100 m/s. It comes to rest after penetrating the sandbag by a distance (d) of 10 cm or 0.1 m.
The work done by the sand's resistive force (F) equals the change in kinetic energy of the bullet. So, F × d = ½ × m × v2. Plugging in the values, we get:
F × 0.1 = ½ × 0.05 × 1002
Solving for F gives us a resistive force of 2500 N.
To calculate the time (t) it takes for the bullet to come to rest, we'll use the equation v = at, where 'a' is the deceleration experienced by the bullet. The work-energy theorem can be used again to find the deceleration: F = m × a.
Thus, 2500 = 0.05 × a, which gives us an acceleration of 50000 m/s2 (but with a negative sign since it's a deceleration). Using v = at, we get:
100 = 50000 × t
This yields a time of 0.002 seconds or 2 milliseconds for the bullet to come to rest.