a rifle bullet with mass 8.00 g strikes and embeds itself in a block with a mass of .992 kg that rests on a frictionless, horizontal surface and it attached to a coil spring. the impact compresses the spring 15.0 cm. calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.250 cm. find the magnitude of the block's velocity just after impact and the initial speed of the bullet.

The magnitude of the block's velocity just after impact is about 2.60 m/s.The initial speed of the bullet is about 325 m/s[tex]\texttt{ }[/tex]Further explanationNewton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.[tex]\large {\boxed {F = ma }[/tex]F = Force ( Newton )m = Object's Mass ( kg )a = Acceleration ( m )Let us now tackle the problem ![tex]\texttt{ }[/tex]Given:mass of bullet = m₁ = 8.00 gram = 8 × 10⁻³ kgmass of block = m₂ = 0.992 kginitial speed of block = u₂ = 0 m/scompression of spring = x = 15.0 cm = 0.15 mspring constant = k = 0.750 ÷ (2.5 ×10⁻³) = 300 N/mAsked:final speed of block = v₂ = ?initial speed of bullet = u₁ = ?Solution:Let:final speed of the block just after impact = final speed of the bullet just after impact = vFirstly , we will use Conservation of Energy as follows:[tex]Ek = Ep[/tex][tex]\frac{1}{2}(m_1 + m_2)v^2 = \frac{1}{2} k x^2[/tex][tex](m_1 + m_2) v^2 = k x^2[/tex][tex](0.008 + 0.992) v^2 = 300 \times 0.15^2[/tex][tex]v^2 = 6.75[/tex][tex]v = \frac{3}{2}\sqrt{3} \texttt{ m/s}[/tex][tex]v \approx 2.60 \texttt{ m/s}[/tex]The magnitude of the block's velocity just after impact is about 2.60 m/s[tex]\texttt{ }[/tex]Next , we will use Conservation of Momentum Law as follows:[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex][tex]0.008u_1 + 0.992(0) = 0.008(\frac{3}{2}\sqrt{3}) + 0.992(\frac{3}{2}\sqrt{3})[/tex][tex]0.008u_1 = \frac{3}{2}\sqrt{3}[/tex][tex]u_1 \approx 325 \texttt{ m/s}[/tex]The initial speed of the bullet is about 325 m/s[tex]\texttt{ }[/tex]Learn moreImpacts of Gravity : https://brainly.com/question/5330244Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454The Acceleration Due To Gravity : https://brainly.com/question/4189441Newton's Law of Motion: https://brainly.com/question/10431582Example of Newton's Law: https://brainly.com/question/498822[tex]\texttt{ }[/tex]Answer detailsGrade: High SchoolSubject: PhysicsChapter: Dynamics[tex]\texttt{ }[/tex]Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant