derive an equation for the average speed for a vertical projected body
from point of projection to the highest point??
Answers
Answer: Vertical projectile motion
3.2 Vertical projectile motion (ESCJW)
In Grade 11, we studied the motion of objects in free fall and saw that such an object has a constant gravitational acceleration of \(\vec{g}\). We now study the motion of objects that are moving upwards or downwards while experiencing a force due to gravity. We call this projectile motion. We will only consider the case where objects move vertically upwards and/or downwards - meaning that there is no horizontal displacement of the object, only vertical displacement.
When we talk about a projectile we mean a body or particle that is project or launched and then moves under the influence of only gravity.
Motion in a gravitational field
We know from Newton's Law of Universal Gravitation that an object in the Earth's gravitational field experiences a force pulling it towards the centre of the Earth. If this is the only force acting on the object then the object will accelerate towards the centre of the Earth.
A person standing on the Earth's surface will interpret this acceleration as objects always falling downwards.
In Grade 11, we showed that the value of the acceleration due to gravity can be treated as a having a constant magnitude of \(g=\text{9,8}\text{ m·s$^{-2}$}\).
In reality, if you go very far away from the Earth's surface, the magnitude of \(\vec{g}\) would change, but, for everyday problems, we can safely treat it as constant. We also ignore any effects that air resistance (drag) might have.
For the rest of this chapter we will deal only with the case where the force due to gravity is the only force acting on the projectile that is falling. Any projectile can be described as falling, even if its motion is upwards initially.
The initial velocity, \(\vec{v}_i\), that an object has and the acceleration that it experiences are two different quantities. It is very important to remember that the gravitational acceleration is always towards the centre of the Earth and constant, regardless of the direction or magnitude of the velocity.
Projectiles moving upwards or downwards in the Earth's gravitational field always accelerate downwards with a constant acceleration \(\vec{g}\). Note: non-zero acceleration means that the velocity is changing.
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Explanation:
Impulse-Momentum Theorem: When a net. force acts on an object, the impulse of the net. force is equal to the change in momentum of. the object: F ∆t = m−→
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