<< Chapter < Page Chapter >> Page >

Exercises

A ball is thrown up in vertical direction with an initial speed of 40 m/s. Find acceleration of the ball at the highest point.

The velocity of the ball at the highest point is zero. The only force on the ball is due to gravity. The accleration of ball all through out its motion is acceleration due to gravity “g”, which is directed downwards. The acceleration of the ball is constant and is not dependent on the state of motion - whether it is moving or is stationary.

Got questions? Get instant answers now!

A ball is released from a height of 45 m. Find the magnitude of average velocity during its motion till it reaches the ground.

The average velocity is ratio of displacement and time. Here, displacement is given. We need to find the time of travel. For the motion of ball, we consider the point of release as origin and upward direction as positive.

y = u t + 1 2 a t 2 45 = 0 X t + 1 2 X - 10 X t 2 t 2 = 45 5 = 9 t = ± 3 s

Neglecting negative time, t = 3 s. Magnitude of average velocity is :

v avg = 45 3 = 15 m / s

Got questions? Get instant answers now!

A ball is released from an elevator moving upward with an acceleration 3 m / s 2 . What is the acceleration of the ball after it is released from the elevator ?

On separation, ball acquires the velocity of elevator – not its acceleration. Once it is released, the only force acting on it is that due to gravity. Hence, acceleration of the ball is same as that due to gravity.

a = 10 m s 2 downward

Got questions? Get instant answers now!

A ball is released from an elevator moving upward with an acceleration 5 m / s 2 . What is the acceleration of the ball with respect to elevator after it is released from the elevator ?

On separation, ball acquires the velocity of elevator – not its acceleration. Once it is released, the only force acting on it is that due to gravity. Hence, acceleration of the ball is same as that due to gravity. The relative acceleration of the ball (considering downward direction as positive) :

a rel = a ball - a elevator a rel = 10 - 5 = 15 m s 2

Got questions? Get instant answers now!

A balloon ascends vertically with a constant speed for 5 second, when a pebble falls from it reaching the ground in 5 s. Find the speed of balloon.

The velocity of balloon is constant and is a measured value. Let the ball moves up with a velocity u. At the time of release, the pebble acquires velocity of balloon. For the motion of pebble, we consider the point of release as origin and upward direction as positive. Here,

y = v t = - u X 5 = - 5 u ; u = u ; a = - g ; t = 5 s

Using equation for displacement :

y = u t + 1 2 a t 2 - 5 u = u X 5 + 1 2 X g X 5 2 10 u = 5 X 25 u = 5 m s

Got questions? Get instant answers now!

A balloon ascends vertically with a constant speed of 10 m/s. At a certain height, a pebble falls from it reaching the ground in 5 s. Find the height of ballon when pebble is released from the balloon.

The velocity of balloon is constant. Let the ball moves up with a velocity u. At the time of release, the pebble acquires velocity of balloon. For the motion of pebble, we consider the point of release as origin and upward direction as positive. Here,

y = ? ; u = 10 m / s ; a = - g ; t = 5 s

Using equation for displacement :

y = u t + 1 2 a t 2 y = 10 X 5 + 1 2 X g X 5 2 y = 50 5 X 25 y = - 75 m

Height of ballon when pebble is released from it,

H = 75 m

Got questions? Get instant answers now!

A ball is released from a top. Another ball is dropped from a point 15 m below the top, when the first ball reaches a point 5 m below the top. Both balls reach the ground simultaneously. Determine the height of the top.

We compare motion of two balls under gravity, when second ball is dropped. At that moment, two balls are 10 m apart. The first ball moves with certain velocity, whereas first ball starts with zero velocity.

Let us consider downward direction as positive. The velocity of the first ball when it reaches 10 m below the top is :

v 2 = u 2 + 2 a x v 2 = 0 + 2 X 10 X 5 v = 10 m / s

Let the balls take time “t” to reach the gorund. First ball travels 10 m more than second ball. Let 1 and 2 denote first and second ball, then,

10 + 10 t + 1 2 X 10 t 2 = 1 2 X 10 t 2 10 t = 10 t = 1 s

In this time, second ball travels a distance given by :

y = 1 2 X 10 t 2 = 5 X 12 = 5 m

But, second ball is 15 m below the top. Hence, height of the top is 15 + 5 = 20 m.

Got questions? Get instant answers now!

One ball is dropped from the top at a height 60 m, when another ball is projected up in the same line of motion. Two balls hit each other 20 m below the top. Compare the speeds of the ball when they strike.

For the motion of first ball dropped from the top, let downward direction be positive :

v 1 = u + a t v 1 = a t = 10 t

For the ball dropped from the top,

x = u t + 1 2 a t 2 - 20 = 0 X t + 1 2 X - 10 X t 2 20 = 5 t 2 t = ± 2 s

Neglecting negative value, t = 2s. Hence, velocity of the ball dropped from the top is :

v 1 = 10 t = 10 X 2 = 30 m / s

For the motion of second ball projected from the bottom, let upward direction be positive :

v 2 = u + at v 2 = u - 10 X 2 = u - 20

Clearly, we need to know u. For upward motion,

x = u t + 1 2 a t 2 40 = u X 2 + 1 2 X - 10 X 2 2 40 = 2 u - 20 = 30 m / s v 2 = 30 20 = 10 m / s

Thus,

v 1 v 2 = 20 10 = 2 1

Got questions? Get instant answers now!

See module titled “ Vertical motion under gravity (application) for more questions.

Questions & Answers

what is defense mechanism
Chinaza Reply
what is defense mechanisms
Chinaza
I'm interested in biological psychology and cognitive psychology
Tanya Reply
what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask