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MatinSAR

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- Homework Statement
- A projectile is fired at an angle of 45° with initial kinetic energy ##E_0##. At the top of its trajectory, the projectile explodes with additional energy ##E_0## into two fragments. One fragment of mass ##m_1## travels straight down. What is the velocity (magnitude and direction) of the second fragment of mass ##m_2## and the velocity of the first? What is the ratio of ##m_1/m_2## when ##m_1## is a maximum?

- Relevant Equations
- Conservation of energy and momentum.

I am going to use this coordinate system:

According to the answer of the book, I think no force is acting on this projectile:

Let's say at top of it's trajectory its velocity is ##u##.

Conservation of energy : $$2E_0=\frac 1 2 m_1 v_1^2+\frac 1 2 m_2 v_2^2$$

Conservation of momentum in x-direction: $$ (m_1+m_2)u = m_2v_2 \cos \theta $$

Conservation of momentum in y-direction: $$ m_2v_2 \sin \theta = m_1 v_1$$

I should find ##v_1## and ##v_2## and ##\theta##. But I failed. Are my equations wrong? Any help would be appreciated.

According to the answer of the book, I think no force is acting on this projectile:

Let's say at top of it's trajectory its velocity is ##u##.

Conservation of energy : $$2E_0=\frac 1 2 m_1 v_1^2+\frac 1 2 m_2 v_2^2$$

Conservation of momentum in x-direction: $$ (m_1+m_2)u = m_2v_2 \cos \theta $$

Conservation of momentum in y-direction: $$ m_2v_2 \sin \theta = m_1 v_1$$

I should find ##v_1## and ##v_2## and ##\theta##. But I failed. Are my equations wrong? Any help would be appreciated.

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