# Projectile Explosion: Finding the Larger Mass's Landing Spot

• h.a.y.l.e.y
In summary: The second term on the right hand side is the change in momentum for the smaller mass, which will be pointing in the opposite direction. So, the larger mass will land about 3.5 meters away from the origin, based on the information given.
h.a.y.l.e.y
I have a problem where I am told a projectile explodes at a distance L (in the x direction) into 2 pieces of masses 1/4 and 3/4. The smaller mass lands back at the origin. Where does the larger mass land?

I have tried CofM arguments but think I need to find the time it takes to reach the top of its trajectory in order to find how long it takes for the masses to land. By the way, I am not told the angle it is fired at.
Could someone enlighten me further please...

Last edited:
h.a.y.l.e.y said:
I have a problem where I am told a projectile explodes at a distance L (in the x direction) into 2 pieces of masses 1/4 and 3/4. The smaller mass lands back at the origin. Where does the larger mass land?

I have tried CofM arguments but think I need to find the time it takes to reach the top of its trajectory in order to find how long it takes for the masses to land. By the way, I am not told the angle it is fired at.
Could someone enlighten me further please...

If you take advantage of the symmetry of projectile motion, conservation of momentum will tell you the change in velocity of both objects at the point of explosion in terms of the velocity just before the explosion . If you write the initial velocity algebraically, you can express the vertical height and the velocity in terms of horizontal postion, x, and initial velocity components, eliminating time from the equations. You are correct that to get a numerical result you would need more specific information, but you can get an algebraic result for the time of flight after the explosion in terms of the initial velocity components and L. Using that time, and the post-explosing horizontal velocity you can calculate the landing point of the larger mass. The algebra gets a bit involved, but there is nothing worse than solving a quadratic equation.

With no external forces acting, momentum is conserved:

$$m\vec{v_i} = m\vec{v_f}$$

What Dan's saying is that the center of mass' momentum will continue to travel in the same direction, so if it breaks into two pieces,

$$m_1\vec{v_i} + m_2\vec{v_i} = m_1\vec{v_f} + m_2\vec{v_f}$$

In the above equation, you know the left hand side, and th first term on the right hand side.

## 1. How does the mass of a projectile affect its landing spot?

The mass of a projectile directly affects its trajectory and landing spot. A heavier mass will have a greater force of gravity acting on it, causing it to travel further and land at a different spot compared to a lighter mass.

## 2. What factors besides mass can affect the landing spot of a projectile explosion?

Other factors that can affect the landing spot of a projectile explosion include the angle of launch, air resistance, and the presence of external forces such as wind or obstacles.

## 3. How is the landing spot of a projectile explosion calculated?

The landing spot of a projectile explosion can be calculated using mathematical formulas that take into account the mass, angle of launch, initial velocity, and other relevant factors. Alternatively, it can also be determined through experimentation and using tools such as a ballistic pendulum.

## 4. Can the landing spot of a projectile explosion be predicted accurately?

While the landing spot of a projectile explosion can be calculated or estimated, it is difficult to predict with 100% accuracy due to the various factors that can affect it. However, with precise measurements and accurate calculations, the predicted landing spot can be very close to the actual landing spot.

## 5. How can the landing spot of a projectile explosion be used in real-life applications?

The calculation of a projectile explosion's landing spot can be useful in various fields such as ballistics, engineering, and even sports. It can help determine the range and accuracy of a projectile, as well as the potential impact of an explosion. It can also be used in designing structures or equipment that can withstand the force of projectile explosions.

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