# Projectile Motion/Dropping an object from the sky

• Amber430
In summary, the question is asking for the time it takes for the fish's speed to double, which is determined by when the vertical component of its velocity is equal to the square root of three times its horizontal component. This can be found by setting up an equation and solving for the time. There is no need to consider the acceleration or displacement since the horizontal velocity remains constant.
Amber430
An eagle is flying horizontally at 7.9 m/s with a fish in its claws. It accidentally drops the fish.

(a) How much time passes before the fish's speed doubles?

(b) How much additional time would be required for the fish's speed to double again?

Initial velocity in the x direction is 7.9m/s. I assumed final velocity in x direction was 7.9m/s and acceleration was 0. But when I use the equations to find one of the other unknown variables everything cancels out and I get zero. There is an example in the book, but it gives the height the fish is dropped from. I feel like I need to know another variable in order to solve this.

Are you sure you're reading the question right? If the fish is in free fall the only acceleration on it is due to gravity. The speed in the x direction will NEVER double unless there is some acceleration in the x direction.

The distance may double if you assume it can fall long enough, perhaps that is what the question is after.

That's what I did. I had Ax=0 m/s^2, Vix= 7.9 m/s, Ay= -9.8 and Viy= 0 m/s and when I plug them into any equation it is always zero

I can find either displacement or time. With either one I get 0.

Vf= Vi + at --> 7.9= 7.9 + (0)t
Vf^2= Vi^2 + 2ax --> 7.9^2= 7.9^2 + 2(0)x

Amber430 said:
I can find either displacement or time. With either one I get 0.

Vf= Vi + at --> 7.9= 7.9 + (0)t
Vf^2= Vi^2 + 2ax --> 7.9^2= 7.9^2 + 2(0)x

What are you finding the displacement of or what would you be finding the time of?

(a) How much time passes before the fish's speed doubles?

(b) How much additional time would be required for the fish's speed to double again?

Amber430 said:
(a) How much time passes before the fish's speed doubles?

(b) How much additional time would be required for the fish's speed to double again?

If the eagle is flying completely horizontal at 7.9m/s when it drops the fish then its speed in the horizontal will remain constant; it will never double. The fish could sail through free space for eternity and it's speed will remain 7.9m/s.

The question would make more sense if the 7.9m/s was downwards and the eagle let go. Because then you're finding out how long it takes the acceleration due to gravity to speed up the fish from -7.9m/s to -15.8m/s.

What they are asking in this problem is at what time does the speed double?

Speed is the |velocity|.

Hence if Vx is invariant, the magnitude of the velocity vector will be when

Vy is equal to (√3)*Vx ---> Vx² + ((√3)*Vx )² = (1 + 3)*Vx² = 4*Vx² ---> |New V| = 2*|Vx|

So all you need to determine is how long until the Vy is (√3)*Vx

## 1. What is projectile motion?

Projectile motion is the motion of an object that is moving through the air or space under the influence of gravity. It follows a curved path known as a parabola.

## 2. What factors affect the trajectory of a dropped object?

The trajectory of a dropped object is affected by the initial velocity, the angle at which it is dropped, and the force of gravity. Air resistance can also play a role in altering the trajectory.

## 3. How does the mass of the object affect its motion when dropped?

The mass of an object does not affect its motion when dropped from the same height. This is because all objects, regardless of their mass, fall at the same rate due to the force of gravity.

## 4. Can an object be dropped from a height without any initial velocity?

Yes, an object can be dropped from a height without any initial velocity. In this case, the object will only be affected by the force of gravity and will fall straight down.

## 5. How can the trajectory of a dropped object be predicted?

The trajectory of a dropped object can be predicted using mathematical equations that take into account the initial velocity, angle of release, and gravitational force. These equations can be solved to determine the height, distance, and time of flight for the object.

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