I believe you need to understand the basic concept common to the four problems and a general method to solve them. This is what I intend to clarify in my answer here.
When any object is thrown in the air, the movement of that object can be resolved in two separate movements:
- Movement along a direction parallel to the earth, or any horizontal surface like a playground or surface of water in a swimming pool.
- Movement in a vertical direction.
Assuming that there is no air resistance to the movement to the object, the horizontal movement under the influence of initial horizontal velocity is uniform at that velocity.
However the vertical component of the velocity of vertical movement is affected by acceleration due to gravity, which on earth is equal to about 9.81 meters/second^2. Depending on initial direction in which the object is thrown the initial velocity vertical velocity can be in upward direction or downward direction. For objects thrown in a horizontal direction or just dropped from a height,this initial velocity can also be zero. A object with initial velocity in upward direction will start rising up, but with reducing velocity because of acceleration due to gravity. In this way the object will continue to rise till its velocity becomes zero. This is the highest point reached by the object. Immediately on reaching its highest point the object start falling down with increasing velocity. With the velocity at highest point being 0 (zero). The object continues to fall till it reaches ground or some other obstruction in its path.
Frequently the Object may be bounced off the surface it hits this way, and may continue to move further. However normally in problems of this type, designed to provide provide practice in use of principles of projectiles, the movement after the object hits the ground is not considered.
The exact path path of motion of the object is the combined effect of the vertical and horizontal movement. In science this path is sometimes called a projectile, which has the shape of a parabola.
In solving problems of this type the horizontal and vertical components of initial velocity can be determine by the following formulas:
Horizontal velocity = Actual velocity*Cos A
Vertical velocity = Actual velocity*Sign A
Where A is the angle that the initial velocity makes with the horizontal.
If horizontal velocity (H) and vertical velocity (V) are known the resultant velocity (R) can be calculated as:
R = (H^2 +V^2)^1/2
The tan of angle A of the resultant velocity can be calculated as:
Tan A = H/R
Further quantities as required by the problem can be calculated using Newton's law of motion and the following equations giving relationship between different variables involved.
v = u + a*t
Average velocity = (u + v)/t
s = u*t + 1/2[a*(t^2)]
v^2 = u ^2 = 2a*s
Where:
u = initial velocity
v = final velocity (after time t)
a = acceleration
f = m*a
In case of acceleration due to gravity the symbol g may be used instead of a.
t = time of movement
s = distance covered (in time t)
f = force applied to accelerate the object
m = bass of the object
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