# Free fall with horizontal velocity

• skiwolf
In summary, the spacecraft's horizontal velocity after 2 seconds is -19.6 meters/second and after 3 seconds is -29.4 meters/second.
skiwolf

## Homework Statement

An airplane releases a spacecraft , after 2 seconds the spacecraft s engine starts providing it with a horizontal velocity of 6m/s relative to the aircraft. What is the magnitude and direction of the velocity after 2 seconds? After 3? Assume the spacecraft is in free-fall in the y direction.

x=vit+1/2at^2
y=-1/2gt^2

## The Attempt at a Solution

It seemed pretty easy... Plug t=2 into the y equation and get a y displacement of 19.6 meters. Then plug in t=3 and arrive at a y displacement of 44.2m, and an x displacement of 3m. Then take the arctan(44.19/3) to get an angle of -86 degrees. The problem is that the answer book appears to split the reference frame at t=2. They say that the y displacement between 2 and 3 seconds is only 4.91m. This doesn't make sense because the object should continue to accelerate downward regardless of the change in x acceleration. I would just assume that this was an error in the answer book, but that would be 3 in a row, and I don't trust myself that much. Any help would be appreciated.

Don't you want instantaneous velocity?

After 2 seconds won't the dropping V be -19.6 m/s

After 3 horizontal will be 3 and vertical -g*t = -29.4 m/s

And overall |V| will be (32 +29.42)1/2 and direction via arc tan?

LowlyPion said:
Don't you want instantaneous velocity?

After 2 seconds won't the dropping V be -19.6 m/s

After 3 horizontal will be 3 and vertical -g*t = -29.4 m/s

I know I'm nit-picking, but doesn't the problem state that the spacecraft is falling in the y direction. So those speed should be positive.

It doesn't really matter so long as the direction chosen as positive is maintained through out.

I merely continued to use the direction already indicated by the OP's equation for y.

In general my preference is usually positive up anyway.

nah, looking for displacement, and your answer doesn't match their's anyway. They still get a total displacement of 19.6 meters to t=2. But looking at it more, they ignore the acceleration of the object over the first two seconds when calculating displacement over (2,3)

skiwolf said:
nah, looking for displacement, and your answer doesn't match their's anyway. They still get a total displacement of 19.6 meters to t=2. But looking at it more, they ignore the acceleration of the object over the first two seconds when calculating displacement over (2,3)

Are you looking for displacement or velocity? The original problem says velocity doesn't it?

As to my equation I see that I took the horizontal V to be 3 and in rereading the problem I see that should have been 6m/s at 3s.

doh... i miscopied the problem... that should say displacement after 2 seconds, sorry about that. Anyway, I talked to the professor, it was an answer book error, thanks for trying anyway.

## 1. What is free fall with horizontal velocity?

Free fall with horizontal velocity is a type of motion where an object falls under the influence of gravity while also moving horizontally at a constant speed. This means that the object is not being slowed down or sped up by any external forces, and is only affected by the force of gravity.

## 2. What causes an object to experience free fall with horizontal velocity?

An object experiences free fall with horizontal velocity when it is launched with a horizontal initial velocity and the force of gravity is the only force acting on it. This can happen when an object is thrown or launched from a high point, such as a cliff or a tall building.

## 3. How does the horizontal velocity affect the motion of an object in free fall?

The horizontal velocity of an object in free fall does not affect its vertical motion. This means that the object will continue to fall towards the ground at a constant rate, regardless of its horizontal velocity. However, the horizontal velocity will determine the distance the object travels horizontally before hitting the ground.

## 4. What is the formula for calculating the distance traveled in free fall with horizontal velocity?

The formula for calculating the distance traveled in free fall with horizontal velocity is d = vt, where d is the distance, v is the horizontal velocity, and t is the time. This formula assumes that the acceleration due to gravity is constant and the object is launched from a high point.

## 5. Can an object experience free fall with horizontal velocity on Earth?

Yes, an object can experience free fall with horizontal velocity on Earth. As long as the object is launched with a horizontal initial velocity and the force of gravity is the only force acting on it, it will follow a parabolic path and experience free fall with horizontal velocity until it hits the ground. This is why objects like baseballs and projectiles follow a curved path when thrown or launched.

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