# Two Objects, Constant Acceleration, 1D Forces, Collision Question

• Hotsuma
In summary, the problem involves a ball being dropped from a 50.0 m-high cliff and a stone being thrown straight up from the bottom of the cliff with a speed of 21.0 m/s. They collide part way up and the question is to determine the common impact time and height. The equations for one-dimensional motion can be used to solve for the time and height, but setting them equal to each other does not yield a solution. Further guidance is needed to solve the problem.
Hotsuma

## Homework Statement

A ball is dropped from the top of a 50.0 rm m-high cliff. At the same time, a carefully aimed stone is thrown straight up from the bottom of the cliff with a speed of 21.0 m/s. The stone and ball collide part way up.

## Homework Equations

v = v0+at
x = x0 + v0t + (1/2)at2
v2 = v20+2a(x- x0)

## The Attempt at a Solution

Two objects, each with different components of one-dimensional motion. The two objects will share a common impact time because they are put into motion at the same time. I have tried solving for time and setting the equations equal to each other, but this yields no result because when I arrange the quadratic formula it evaluates to y = 0, which doesn't make sense. I don't need explicit help (although I don't mind, I just hate typing this out so I don't expect people trying to help me to), I just need a direction to take this problem.

Thanks

What is the question?

If they collide there are two things that must be equal.

Time. and Height.

## 1. What is the equation for calculating the acceleration of two objects?

The equation for calculating acceleration of two objects is a = (v2 - v1) / t, where a is acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time interval.

## 2. How do you determine the net force acting on an object?

To determine the net force acting on an object, you must add up all the individual forces acting on the object, taking into account their direction and magnitude. This is known as the vector sum of forces.

## 3. What happens to the kinetic energy of two objects during a collision?

During a collision, the kinetic energy of the two objects may change. If the objects stick together, the kinetic energy will decrease due to the loss of velocity. If the objects bounce off each other, the kinetic energy will remain the same, but may be redistributed between the two objects.

## 4. Can two objects with different masses have the same acceleration?

Yes, two objects with different masses can have the same acceleration if the net force acting on them is the same. This is demonstrated by Newton's Second Law of Motion, which states that acceleration is directly proportional to the net force and inversely proportional to the mass of an object.

## 5. How does the direction of force affect the motion of an object?

The direction of force affects the motion of an object by changing its velocity. If the force is in the same direction as the object's motion, it will increase its speed. If the force is in the opposite direction, it will decrease its speed. If the force is perpendicular to the object's motion, it will cause the object to change its direction of motion.

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