How Fast to Launch an Object from Mercury for a Final Speed of 3000 m/s?

In summary, the radius of Mercury is 2440 km and its mass is 0.3x10^24 kg. To achieve a final speed of 3000 m/s, an initial speed of 4151.8315 m/s is needed when launching an object straight up from just above the atmosphere of Mercury. The formula used is vi² = vf² + GM/ri, where GM/ri is the missing factor of kinetic energy.
  • #1
ohheytai
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The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440x10^3 m), and its mass is 0.3x10^24 kg. An object is launched straight up from just above the atmosphere of Mercury.

(a) What initial speed is needed so that when the object is far from Mercury its final speed is 3000 m/s?


Homework Equations


vi² = vf² + GM/ri


The Attempt at a Solution


i got 4151.8315 m/s
and its wrong help me please!
 
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  • #2
ohheytai said:

Homework Equations


vi² = vf² + GM/ri
The kinetic energy of an object is (1/2)mv2. Do you see what is missing in your formula?

The Attempt at a Solution


i got 4151.8315 m/s
and its wrong help me please!
 

Related to How Fast to Launch an Object from Mercury for a Final Speed of 3000 m/s?

What is the Initial Speed?

The initial speed, also known as the initial velocity, is the starting velocity of an object in motion. It is the speed at which an object begins to move.

How is Initial Speed calculated?

The initial speed is calculated by dividing the change in distance by the change in time. This can be represented by the equation initial speed = (final distance - initial distance) / (final time - initial time). It can also be calculated by taking the square root of 2 multiplied by the acceleration multiplied by the distance traveled.

What is the difference between Initial Speed and Average Speed?

The initial speed is the speed of an object at the beginning of its motion, while average speed is the total distance traveled divided by the total time taken. Average speed takes into account any changes in speed throughout the motion, while initial speed only represents the starting speed.

Why is Initial Speed important?

Initial speed is important because it is a key factor in determining the motion of an object. It can help predict the future position and speed of an object, as well as its acceleration and overall motion. It is also useful in analyzing the effects of forces on an object.

How does air resistance affect Initial Speed?

Air resistance can decrease the initial speed of an object by slowing it down. This is due to the friction between the object and the air molecules as it moves through the air. The amount of air resistance depends on the shape and surface area of the object, as well as the density of the air and the speed of the object.

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