that a ball is dropped from the upper observation deck of a building, 350 m above the ground. hat is the velocity of the ball after 7 seconds? w fast is the ball traveling when it hits the ground? ON need to find the velocity both when t = 7 and when the ball hits the ground, so it's efficient to start by finding the velocity at a general time t=a. Using the equation of motion = 4.9t, we have the following. lim lim lim f(a+h)-f(a) h 4.9 h 4.9(a² + 2ah+h² h lim 4.9 4.98² =9.8( [ e velocity, in m/s, after 7 seconds is v(7) = ce the observation deck is 350 m above the ground, the ball will hit the ground at the time t, in seconds, when s(t) = 350, that is, we have the following.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
![Suppose that a ball is dropped from the upper observation deck of a building, 350 m above the ground.
(a) What is the velocity of the ball after 7 seconds?
(b) How fast is the ball traveling when it hits the ground?
SOLUTION
We will need to find the velocity both when t = 7 and when the ball hits the ground, so it's efficient to start by finding the velocity at a general time t = a. Using the equation of motion
s = f(t) = 4.9t², we have the following.
v(a) = lim
h→0
= lim
= lim
h-o
= lim
h→0
f(a+h)-f(a)
h
2² =
4.9
=lim 4.9
h
4.9(² + 2ah + h²-a²)
h
t =
(a) The velocity, in m/s, after 7 seconds is v(7) = 9.8( [
(b) Since the observation deck is 350 m above the ground, the ball will hit the ground at the time t, in seconds, when s(t) = 350, that is, we have the following.
4.9t² = 350
This gives the following. (Round your approximation to one decimal place.)
350
4.9
h
and
4.9a²
350
4.9
The velocity of the ball, in m/s, as it hits the ground is the following. (Round your answer to the nearest integer.)
350
v(t) = v
350
=9.8 4.9
4.9
m/s
m/s.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21770dad-69ca-47fc-acb8-f54b4e062415%2Ffca24df4-1417-461a-af6b-ec0e40440dd5%2Fhhk8sk7t_processed.png&w=3840&q=75)
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