How Does Conservation of Energy Determine Initial Speed in Projectile Motion?

In summary, the problem involves a stone being thrown upward at a 53 degree angle with a maximum height of 24m. The stone's initial speed is not given but can be solved using the Conservation of Energy formula. The mass of the stone is not needed in the calculation.
  • #1
maniacp08
115
0
A stone is thrown upward at an angle of 53 degrees above the horizontal. Its maximum height above the release point is 24m. What was the stone's initial speed?
Assume any effects of air resistance are negligible.

This problem is to be solved using Conservation of Energy.

Since there is no external force nor non-conservative forces present, this is just the change in mechanical energy.

Uf + Kf = Ui + Ki
mgh + 0 = 0 + 1/2 mv^2
=mgh = 1/2 mv^2
where y = 0 at the horizontal.

I got stuck because the mass of the stone is not given. Is my approach wrong?
 
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  • #2
Divide both sides of your last line by the mass. Notice that the mass cancels out of the equation! You don't need to know it.
 
  • #3
Doh!
Thanks for pointing that out.
 

What is conservation of energy?

Conservation of energy is a fundamental law of physics that states energy cannot be created or destroyed, only transformed from one form to another. This means that the total energy in a closed system remains constant over time.

Why is conservation of energy important?

Conservation of energy is important because it allows us to understand and predict the behavior of physical systems. It helps us to conserve resources and minimize waste, as well as providing a basis for many technological advancements.

How does conservation of energy apply to everyday life?

Conservation of energy applies to everyday life in many ways. For example, when we turn on a light bulb, electrical energy is converted into light and heat energy. When we ride a bike, our pedaling energy is converted into kinetic energy. It also applies to the food we eat, as our bodies convert the chemical energy in food into energy for our daily activities.

What are some examples of energy conservation methods?

Some examples of energy conservation methods include using energy-efficient appliances and vehicles, turning off lights and electronics when not in use, adjusting thermostats to save on heating and cooling, and using renewable energy sources such as solar or wind power.

Is conservation of energy always true?

Yes, conservation of energy is always true in a closed system. However, in an open system where energy can enter or leave, the total energy may not remain constant. In such cases, the law of conservation of mass and energy applies, stating that the total mass and energy in a system will remain constant.

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