ayrestaurant said:Homework Statement
A baseball is thrown upward from a height of 2m with an initial velocity of 10m/s. Determine its maximum height.
Homework Equations
S(0) = 2m
S'(0) = 10m/s
The Attempt at a Solution
S'(t) = -32t + 10
S(t) = -16t^2 + 10t + 2
I know that if you equal s(t) = 0 you get time, but how do I get maximum height?
Thanx in advanced!
berkeman said:The easiest way would be to use energy conservation. Are you familiar with the equation:
TE = PE + KE (total energy is equal to potential energy plus kinetic energy)
What is the KE at the top of the object's travel?
Integration is a mathematical concept that involves finding the area under a curve. It is used to solve various problems in mathematics, physics, and engineering.
To determine the maximum height using integration, you first need to represent the height as a function of time. Then, you need to find the derivative of this function and set it equal to zero to find the stationary points. The maximum height can be found by substituting the value of time at the stationary point into the original function.
Yes, integration can be used to find the maximum height of any object, as long as the height can be represented as a function of time.
The units of maximum height obtained through integration will depend on the units used in the function representing the height. For example, if the height is represented in meters and time in seconds, the maximum height will have units of meters.
Yes, there are limitations to using integration to determine maximum height. This method assumes that the object is moving in a straight line and does not take into account factors such as air resistance and external forces. It is also limited to objects with a constant acceleration, such as freefall or projectile motion.