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A small explosive with m = 5.00 kg is launched at an angle of 0 = 28° to the horizontal with a speed of 25 m/s. After 0.910 s following launch it explodes into two pieces of equal mass with an explosion that releases 790 J of energy. Assume that all the energy of the explosion goes to the kinetic energy of the two pieces and no mass is lost in the explosion. The forward traveling half, mg, is seen to have velocity vg that point exactly along the velocity of the explosive immediately before the explosion. %3D (a) What is the angle the that v4 makes with the horizontal direction? (b) What is the magnitude of velocity of the forward traveling half, vg? (c) How much further will mg travel because of the explosion as compared to the distance the entire explosive would have traveled in the absence of a midair explosion? (d) How far apart will the two halves of the explosive land from each other? V m, m explosion launcher

A small explosive with m = 5.00 kg is launched at an angle of 0 = 28° to the horizontal with a speed of 25 m/s. After 0.910 s following launch it explodes into two pieces of equal mass with an explosion that releases 790 J of energy. Assume that all the energy of the explosion goes to the kinetic energy of the two pieces and no mass is lost in the explosion. The forward traveling half, mg, is seen to have velocity vg that point exactly along the velocity of the explosive immediately before the explosion. %3D (a) What is the angle the that v4 makes with the horizontal direction? (b) What is the magnitude of velocity of the forward traveling half, vg? (c) How much further will mg travel because of the explosion as compared to the distance the entire explosive would have traveled in the absence of a midair explosion? (d) How far apart will the two halves of the explosive land from each other? V m, m explosion launcher

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**Text:** A small explosive with \( m = 5.00 \, \text{kg} \) is launched at an angle of \( \theta = 28^\circ \) to the horizontal with a speed of 25 m/s. After 0.910 s following launch it explodes into two pieces of equal mass with an explosion that releases 790 J of energy. Assume that all the energy of the explosion goes to the kinetic energy of the two pieces and no mass is lost in the explosion. The forward traveling half, \( m_B \), is seen to have velocity \( v_B \) that point exactly along the velocity of the explosive immediately before the explosion. (a) What is the angle that \( v_A \) makes with the horizontal direction? (b) What is the magnitude of velocity of the forward traveling half, \( v_B \)? (c) How much further will \( m_B \) travel because of the explosion as compared to the distance the entire explosive would have traveled in the absence of a midair explosion? (d) How far apart will the two halves of the explosive land from each other? **Diagram Explanation:** The diagram shows a launcher at an angle \( \theta \) from the horizontal, firing a projectile with initial velocity \( v_0 \). The projectile reaches a certain point and then explodes into two masses, \( m_A \) and \( m_B \), each represented by black squares. - **\( m_A \) and \( m_B \):** Two equal masses resulting from the explosion. - **\( v_A \):** The velocity of the backward moving mass \( m_A \). - **\( v_B \):** The velocity of the forward moving mass \( m_B \), shown to continue along the trajectory of the original launch direction. - The explosion is indicated with dashed lines showing the direction and curvature of the projectile's path before and after the explosion. The line for \( v_B \) follows the original trajectory, while the line for \( v_A \) deviates in a different direction.
Transcribed Image Text:**Text:** A small explosive with \( m = 5.00 \, \text{kg} \) is launched at an angle of \( \theta = 28^\circ \) to the horizontal with a speed of 25 m/s. After 0.910 s following launch it explodes into two pieces of equal mass with an explosion that releases 790 J of energy. Assume that all the energy of the explosion goes to the kinetic energy of the two pieces and no mass is lost in the explosion. The forward traveling half, \( m_B \), is seen to have velocity \( v_B \) that point exactly along the velocity of the explosive immediately before the explosion. (a) What is the angle that \( v_A \) makes with the horizontal direction? (b) What is the magnitude of velocity of the forward traveling half, \( v_B \)? (c) How much further will \( m_B \) travel because of the explosion as compared to the distance the entire explosive would have traveled in the absence of a midair explosion? (d) How far apart will the two halves of the explosive land from each other? **Diagram Explanation:** The diagram shows a launcher at an angle \( \theta \) from the horizontal, firing a projectile with initial velocity \( v_0 \). The projectile reaches a certain point and then explodes into two masses, \( m_A \) and \( m_B \), each represented by black squares. - **\( m_A \) and \( m_B \):** Two equal masses resulting from the explosion. - **\( v_A \):** The velocity of the backward moving mass \( m_A \). - **\( v_B \):** The velocity of the forward moving mass \( m_B \), shown to continue along the trajectory of the original launch direction. - The explosion is indicated with dashed lines showing the direction and curvature of the projectile's path before and after the explosion. The line for \( v_B \) follows the original trajectory, while the line for \( v_A \) deviates in a different direction.
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