A bullet penetrating 30cm into its target loses its velocity by 50%. What additional distance will it penetrate into the target before it comes to rest?

Explanation

Let's use the equation of motion to find the additional distance the bullet will penetrate before coming to rest. The equation of motion for an object starting with an initial velocity u and coming to rest after covering a distance s with a constant deceleration a is:v2 = u2 + 2aswhere v is the final velocity.We know that the bullet loses 50% of its velocity after penetrating 30 cm. Let the initial velocity of the bullet be u; then, its final velocity will be 0.5u. So, using the above equation of motion, we can write:(0.5u)2 = u2 + 2a(0.3)Solving for a, we get:a = -3u2/4(0.3)Now, we can use the same equation of motion to find the additional distance the bullet will penetrate before coming to rest. Let the final velocity of the bullet be v, then we have:v2 = (0.5u)2 + 2a(s + 0.3)Since the bullet comes to rest after penetrating the additional distance, we have v = 0. Solving for s, we get:s = (v2 - (0.5u)2)/2a - 0.3Substituting v = 0 and a = -3u2/4(0.3), we get:s = (0.5u)2/(3u2/4(0.3)) - 0.3Simplifying, we get:s = 0.1 m = 10 cmTherefore, the additional distance the bullet will penetrate into the target before coming to rest is 10 cm.