Question
Question: (1) How would I use the kinetic equations to derive a general equation for the time it takes a ball ...
(1) How would I use the kinetic equations to derive a general equation for the time it takes a ball dropped from rest at vertical heighthto reach the ground?
(2) Using the result from the first part, write a general equation for the distance travelled by a projectile that is rolling off a table of height hwith a horizontal velocity v0x.
Solution
In order to answer this question, we will be using the concepts of motion of a body in one dimension. We will also be using the equation of motions to derive our answers. For the second portion, we will be using the concept of a horizontal projectile.
Formula used:
First equation of motion: v=u+at
Second equation of motion: s=ut+21at2
Third equation of motion: v2=u2+2as
Where v is the final velocity, uis the initial velocity, a is the acceleration and t is the time.
Complete step by step answer:
In order to find our answers, we will be considering two different cases
CASE 1:
As we can see from the figure, the ball is dropped vertically downwards from a height h.Now, as the ball is dropped, the initial velocity u of the ball will be zero. After being dropped, the ball will fall down to the ground under the effect of gravitational acceleration g. Therefore, using the second equation of motion, we get