Speed of objects as they hit the ground

In summary, when comparing two objects thrown from the same height with the same initial velocity, the one thrown downward will have a higher final speed due to the acceleration of gravity. However, the velocities at the time of impact will be the same due to energy conservation.
  • #1
yrjosmiel
53
5
Let's say there are two objects. One is thrown directly downward at v0 and the other is thrown horizontally (90 degrees) at v0, both from height h. Which object will have a higher speed by the time they hit the ground? Would they have the same speed?

For the object thrown downward...
h = (vf2 - v02)/2a
vfy axis = sqrt(v02 + 2ah)
final speed = sqrt(v02 + 2ah)

For the object thrown horizontally
vy axis = sqrt(2ah)
vx axis = v0
add the two vectors
vftotal = sqrt(v02 + 2ah)

Is this right? Or have I miscalculated something in the way?
 
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  • #2
You can also use energy conservation here.
 
  • #3
Looks good to me. The matching velocities speeds make sense when you consider conservation of energy.
 
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  • #4
The velocities won't be the same but the speeds will.
 

FAQ: Speed of objects as they hit the ground

1. What factors affect the speed of objects as they hit the ground?

The speed of an object as it hits the ground is affected by several factors, including the height from which it is dropped, the mass of the object, and the presence of air resistance. Objects with a larger mass will fall faster than objects with a smaller mass, and objects dropped from a higher height will have a greater speed upon impact.

2. How does gravity play a role in the speed of objects as they hit the ground?

Gravity is the force that pulls objects towards the center of the Earth. As an object falls, it accelerates due to the force of gravity. This means that the speed of the object increases as it gets closer to the ground. However, once the object reaches its terminal velocity, the force of gravity is balanced by air resistance, resulting in a constant speed.

3. What is terminal velocity and how does it affect the speed of objects as they hit the ground?

Terminal velocity is the maximum speed that an object can reach as it falls through the air. As an object falls, it accelerates due to gravity, but as it gains speed, air resistance also increases. Eventually, the force of air resistance becomes equal to the force of gravity, resulting in a constant speed known as terminal velocity.

4. How does air resistance impact the speed of objects as they hit the ground?

Air resistance is a force that opposes the motion of an object through the air. As an object falls, it experiences an upward force from air resistance, which increases as the object's speed increases. This force eventually becomes equal to the force of gravity, resulting in a constant speed known as terminal velocity.

5. Can the speed of an object as it hits the ground be calculated?

Yes, the speed of an object as it hits the ground can be calculated using the formula V = √(2gh), where V is the speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height from which the object was dropped. However, this calculation does not take into account air resistance, which can significantly affect the speed of the object.

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