How to Calculate Initial Speed and Impact Speed of a Vertically Thrown Stone?

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In summary, the stone is thrown with an initial speed of $u$ m/s and reaches the ground after 5 seconds. Using the equations of motion, we can find the value of $u$ and the speed at which the stone hits the ground. Alternatively, we can use the equation for the height of a projectile to solve for $u$.
  • #1
markosheehan
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a stone us thrown vertically upwards under gravity with a speed of u m/s from a point 30 metres above the horizontal ground. the stone hist the ground 5 seconds later.

(i) find the value if u
(i)find the speed with which the particle hits the ground.

can someone help me work this out. i tried to divide it into 2 different parts. from when the stone is thrown up to when it gets to v=0 and then from when it drops back down to earth. i tried to use uvast equations and i could say the 1st bit has time t and the next bit has 5-t time but the intial speeds are not the same so i don't know what to do
 
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  • #2
You can use the fact that a stone dropped from rest travels distance $\dfrac{gt^2}{2}$ and has speed $gt$ after falling for $t$ seconds (or, conversely, a stone thrown up vertically with speed $gt$ reaches the maximum height after time $t$ and travels distance $\dfrac{gt^2}{2}$). Indeed, the speed increases by $g$ each second, and $\dfrac{gt^2}{2}$ is the area under the graph of speed plotted over time, which is distance.

Suppose, as you do, that the stone took $t$ seconds to reach its maximum height. Then it flew $\dfrac{gt^2}{2}$ meters over the initial position. The distance it traveled on the way down is $\dfrac{g(5-t)^2}{2}$. This allows forming an equation in $t$. Once you know $t$, you can find $u=gt$.

Another way to solve this is to use the fact that a stone thrown vertically upward with speed $u$ from height $h_0$ is at height $h(t)=h_0+ut-\dfrac{gt^2}{2}$ after time $t$. You can equate $h(t)$ to 0 and find $u$ from there.
 

FAQ: How to Calculate Initial Speed and Impact Speed of a Vertically Thrown Stone?

What is the concept of "Stone under gravity"?

The concept of "Stone under gravity" refers to the behavior of a stone or any object when it is under the influence of the force of gravity. This force is what causes objects to fall towards the ground when dropped.

What is the relationship between mass and gravitational force?

The relationship between mass and gravitational force is directly proportional. This means that the greater the mass of an object, the greater the gravitational force it experiences. In other words, the heavier the stone, the stronger the force of gravity pulling it towards the ground.

How does the height of an object affect its gravitational potential energy?

The higher an object is, the greater its gravitational potential energy. This is because the higher an object is, the more potential energy it has due to its position in the Earth's gravitational field. As the object falls towards the ground, this potential energy is converted into kinetic energy.

What factors affect the acceleration of an object under gravity?

The acceleration of an object under gravity is affected by two main factors: the mass of the object and the magnitude of the gravitational force. The greater the mass of the object, the slower its acceleration will be. Similarly, the greater the force of gravity acting on the object, the faster its acceleration will be.

Can the force of gravity be canceled out?

No, the force of gravity cannot be canceled out. It is a fundamental force of nature that is always present and affects all objects with mass. However, the effects of gravity can be counteracted by other forces, such as air resistance or the force of a person pushing against the ground.

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