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An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration due to gravity have the same sign on the way up as on the way down?

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Suppose you throw a rock nearly straight up at a coconut in a palm tree, and the rock misses on the way up but hits the coconut on the way down. Neglecting air resistance, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the coconut on the way up? Is it more likely to dislodge the coconut on the way up or down? Explain.

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If an object is thrown straight up and air resistance is negligible, then its speed when it returns to the starting point is the same as when it was released. If air resistance were not negligible, how would its speed upon return compare with its initial speed? How would the maximum height to which it rises be affected?

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The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration due to gravity being the same, how many times higher could a safe fall on the Moon be than on Earth (gravitational acceleration on the Moon is about 1/6 that of the Earth)?

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How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of g size 12{g} {} on Earth)?

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Problems&Exercises

Assume air resistance is negligible unless otherwise stated.

Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00, (c) 1.50, and (d) 2.00 s for a ball thrown straight up with an initial velocity of 15.0 m/s. Take the point of release to be y 0 = 0 size 12{y rSub { size 8{0} } =0} {} .

(a) y 1 = 6 . 28 m size 12{y rSub { size 8{1} } =6 "." "28 m"} {} ; v 1 = 10 . 1 m/s size 12{v rSub { size 8{1} } ="10" "." "1 m/s"} {}

(b) y 2 = 10 . 1 m size 12{y rSub { size 8{2} } ="10" "." "1 m"} {} ; v 2 = 5 . 20 m/s size 12{v rSub { size 8{2} } =5 "." "20 m/s"} {}

(c) y 3 = 11 . 5 m ; v 3 = 0 .300 m/s size 12{v rSub { size 8{3} } =0 "." "300"" m/s"} {}

(d) y 4 = 10 .4 m ; v 4 = 4 .60 m/s size 12{v rSub { size 8{4} } = - 4 "." "60"" m/s"} {}

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Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00, (c) 1.50, (d) 2.00, and (e) 2.50 s for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water.

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A basketball referee tosses the ball straight up for the starting tip-off. At what velocity must a basketball player leave the ground to rise 1.25 m above the floor in an attempt to get the ball?

v 0 = 4 . 95 m/s size 12{v rSub { size 8{0} } =4 "." "95 m/s"} {}

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A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial velocity of 1.40 m/s and observes that it takes 1.8 s to reach the water. (a) List the knowns in this problem. (b) How high above the water was the preserver released? Note that the downdraft of the helicopter reduces the effects of air resistance on the falling life preserver, so that an acceleration equal to that of gravity is reasonable.

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A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 m/s. (a) List the knowns in this problem. (b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known and identify its value. Then identify the unknown, and discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking units, and discuss whether the answer is reasonable. (c) How long is the dolphin in the air? Neglect any effects due to his size or orientation.

(a) a = 9 . 80 m/s 2 size 12{a= - 9 "." "80 m/s" rSup { size 8{2} } } {} ; v 0 = 13 . 0 m/s size 12{v rSub { size 8{0} } ="13" "." "0 m/s"} {} ; y 0 = 0 m size 12{y rSub { size 8{0} } ="0 m"} {}

(b) v = 0 m/s . Unknown is distance y to top of trajectory, where velocity is zero. Use equation v 2 = v 0 2 + 2 a y y 0 size 12{v rSup { size 8{2} } =v rSub { size 8{0} } rSup { size 8{2} } +2a left (y - y rSub { size 8{0} } right )} {} because it contains all known values except for y , so we can solve for y size 12{y} {} . Solving for y size 12{y} {} gives

v 2 v 0 2 = 2 a y y 0 v 2 v 0 2 2 a = y y 0 y = y 0 + v 2 v 0 2 2 a = 0 m + 0 m/s 2 13.0 m/s 2 2 9.80 m /s 2 = 8.62 m alignl { stack { size 12{v rSup { size 8{2} } - v rSub { size 8{0} } rSup { size 8{2} } =2a left (y - y rSub { size 8{0} } right )} {} #{ {v rSup { size 8{2} } - v rSub { size 8{0} } rSup { size 8{2} } } over {2a} } =y - y rSub { size 8{0} } {} # y=y rSub { size 8{0} } + { {v rSup { size 8{2} } - v rSub { size 8{0} } rSup { size 8{2} } } over {2a} } =0`m+ { { left (0`"m/s" right ) rSup { size 8{2} } - left ("13" "." 0`"m/s" right ) rSup { size 8{2} } } over {2 left ( - 9 "." "80"`"m/s" rSup { size 8{2} } right )} } =8 "." "62"`m {}} } {}

Dolphins measure about 2 meters long and can jump several times their length out of the water, so this is a reasonable result.

(c) 2 . 65 s size 12{2 "." "65 s"} {}

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Questions & Answers

explain the three laws of isaac Newton with the reference
glory Reply
1st law ; a body will continue to stay at a state of rest or continue to move at a uniform motion on a straight line unless an external force is been acted upon
Austine
3rd law; in every action there is an equal or opposite reaction
Austine
2nd law: F=ma
Austine
why am i not having access to the Link in your exemples /figures ?
Augustine Reply
what is circut
hasiya Reply
newtons law of motion
hasiya
First law:In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
Manan
is the ability to do work
Adjah Reply
Energy
Nwany
u from
Hejreen
any body online hain
Hejreen
ability to do work is energy
Irshad
what is energy
Mercy Reply
energy is ability of the capacity to doing work
shafiu
what is vector
mosco Reply
A quantity that has both magnitude and direction
Donaldo
can a body with out mass float in space
mosco
Is the quantity that has both magnitude and direction
Amoah
Yes it can float in space,e.g.polyethene has no mass that's why it can float in space
Amoah
that's my suggestion,any other explanation can be given also,thanks
Amoah
A charge of 1.6*10^-6C is placed in a uniform electric field in a density 2*5^10Nc^-1, what is the magnitude of the electric force exerted on the charge?
Omotosho Reply
what's phenomena
Enoch Reply
Phenomena is an observable fact or event.
Love
Prove that 1/d+1/v=1/f
James Reply
What interference
Moyinoluwa Reply
What is a polarized light called?
Moyinoluwa
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
Biola Reply
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
what's velocity
mosco
Velocity is the rate of change of displacement
Divya
Atomic transmutation
Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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