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Serving at a speed of 170 km/h, a tennis player hits the ball at a height of 2.5 m and an angle θ size 12{θ} {} below the horizontal. The service line is 11.9 m from the net, which is 0.91 m high. What is the angle θ size 12{θ} {} such that the ball just crosses the net? Will the ball land in the service box, whose out line is 6.40 m from the net?

θ = 6.1º size 12{θ} {}

yes, the ball lands at 5.3 m from the net

A football quarterback is moving straight backward at a speed of 2.00 m/s when he throws a pass to a player 18.0 m straight downfield. (a) If the ball is thrown at an angle of 25º size 12{"25°"} {} relative to the ground and is caught at the same height as it is released, what is its initial speed relative to the ground? (b) How long does it take to get to the receiver? (c) What is its maximum height above its point of release?

Gun sights are adjusted to aim high to compensate for the effect of gravity, effectively making the gun accurate only for a specific range. (a) If a gun is sighted to hit targets that are at the same height as the gun and 100.0 m away, how low will the bullet hit if aimed directly at a target 150.0 m away? The muzzle velocity of the bullet is 275 m/s. (b) Discuss qualitatively how a larger muzzle velocity would affect this problem and what would be the effect of air resistance.

(a) −0.486 m

(b) The larger the muzzle velocity, the smaller the deviation in the vertical direction, because the time of flight would be smaller. Air resistance would have the effect of decreasing the time of flight, therefore increasing the vertical deviation.

An eagle is flying horizontally at a speed of 3.00 m/s when the fish in her talons wiggles loose and falls into the lake 5.00 m below. Calculate the velocity of the fish relative to the water when it hits the water.

An owl is carrying a mouse to the chicks in its nest. Its position at that time is 4.00 m west and 12.0 m above the center of the 30.0 cm diameter nest. The owl is flying east at 3.50 m/s at an angle 30.0º size 12{"30º} below the horizontal when it accidentally drops the mouse. Is the owl lucky enough to have the mouse hit the nest? To answer this question, calculate the horizontal position of the mouse when it has fallen 12.0 m.

4.23 m. No, the owl is not lucky; he misses the nest.

Suppose a soccer player kicks the ball from a distance 30 m toward the goal. Find the initial speed of the ball if it just passes over the goal, 2.4 m above the ground, given the initial direction to be 40º size 12{"40" rSup { size 8{o} } } {} above the horizontal.

Can a goalkeeper at her/ his goal kick a soccer ball into the opponent’s goal without the ball touching the ground? The distance will be about 95 m. A goalkeeper can give the ball a speed of 30 m/s.

No, the maximum range (neglecting air resistance) is about 92 m.

The free throw line in basketball is 4.57 m (15 ft) from the basket, which is 3.05 m (10 ft) above the floor. A player standing on the free throw line throws the ball with an initial speed of 7.15 m/s, releasing it at a height of 2.44 m (8 ft) above the floor. At what angle above the horizontal must the ball be thrown to exactly hit the basket? Note that most players will use a large initial angle rather than a flat shot because it allows for a larger margin of error. Explicitly show how you follow the steps involved in solving projectile motion problems.

In 2007, Michael Carter (U.S.) set a world record in the shot put with a throw of 24.77 m. What was the initial speed of the shot if he released it at a height of 2.10 m and threw it at an angle of 38.0º size 12{"38"º} {} above the horizontal? (Although the maximum distance for a projectile on level ground is achieved at 45º size 12{"45"º} {} when air resistance is neglected, the actual angle to achieve maximum range is smaller; thus, 38º size 12{"38"º} {} will give a longer range than 45º size 12{"45"º} {} in the shot put.)

15.0 m/s

A basketball player is running at 5 . 00 m/s size 12{5 "." "00 m/s"} {} directly toward the basket when he jumps into the air to dunk the ball. He maintains his horizontal velocity. (a) What vertical velocity does he need to rise 0.750 m above the floor? (b) How far from the basket (measured in the horizontal direction) must he start his jump to reach his maximum height at the same time as he reaches the basket?

A football player punts the ball at a 45.0º size 12{"45"°} {} angle. Without an effect from the wind, the ball would travel 60.0 m horizontally. (a) What is the initial speed of the ball? (b) When the ball is near its maximum height it experiences a brief gust of wind that reduces its horizontal velocity by 1.50 m/s. What distance does the ball travel horizontally?

(a) 24.2 m/s

(b) The ball travels a total of 57.4 m with the brief gust of wind.

Prove that the trajectory of a projectile is parabolic, having the form y = ax + bx 2 size 12{y= ital "ax"+ ital "bx" rSup { size 8{2} } } {} . To obtain this expression, solve the equation x = v 0 x t size 12{x=v rSub { size 8{0x} } } {t} for t size 12{t} {} and substitute it into the expression for y = v 0 y t ( 1 / 2 ) gt 2 size 12{y=υ rSub { size 8{0y} } t \( 1/2 \) ital "gt" rSup { size 8{2} } } {} (These equations describe the x size 12{x} {} and y size 12{y} {} positions of a projectile that starts at the origin.) You should obtain an equation of the form y = ax + bx 2 size 12{y= ital "ax"+ ital "bx" rSup { size 8{2} } } {} where a size 12{a} {} and b size 12{b} {} are constants.

Derive R = v 0 2 sin 0 g size 12{R= { {v rSub { size 8{0} } rSup { size 8{2} } "sin"2θ rSub { size 8{0} } } over {g} } } {} for the range of a projectile on level ground by finding the time t size 12{t} {} at which y size 12{y} {} becomes zero and substituting this value of t size 12{t} {} into the expression for x x 0 size 12{x - x rSub { size 8{0} } } {} , noting that R = x x 0 size 12{R=x - x rSub { size 8{0} } } {}

y y 0 = 0 = v 0 y t 1 2 gt 2 = ( v 0 sin θ ) t 1 2 gt 2 size 12{y - y rSub { size 8{0} } =0=v rSub { size 8{0y} } t - { {1} over {2} } ital "gt" rSup { size 8{2} } = \( v rSub { size 8{0} } "sin"θ \) t - { {1} over {2} } ital "gt" rSup { size 8{2} } } {} ,

so that t = 2 ( v 0 sin θ ) g size 12{t= { {2 \( v rSub { size 8{0} } "sin"θ \) } over {g} } } {}

x x 0 = v 0 x t = ( v 0 cos θ ) t = R , size 12{x - x rSub { size 8{0} } =v rSub { size 8{0x} } t= \( v rSub { size 8{0} } "cos"θ \) t=R,} {} and substituting for t size 12{t} {} gives:

R = v 0 cos θ 2 v 0 sin θ g = 2 v 0 2 sin θ cos θ g size 12{R=v rSub { size 8{0} } "cos"θ left ( { {2v rSub { size 8{0} } "sin"θ} over {g} } right )= { {2v rSub { size 8{0} rSup { size 8{2} } } "sin"θ"cos"θ} over {g} } } {}

since 2 sin θ cos θ = sin , size 12{2"sin"θ"cos"θ="sin"2θ,} {} the range is:

R = v 0 2 sin g size 12{ {underline {R= { {v rSub { size 8{0} rSup { size 8{2} } } "sin"2θ} over {g} } }} } {} .

Unreasonable Results (a) Find the maximum range of a super cannon that has a muzzle velocity of 4.0 km/s. (b) What is unreasonable about the range you found? (c) Is the premise unreasonable or is the available equation inapplicable? Explain your answer. (d) If such a muzzle velocity could be obtained, discuss the effects of air resistance, thinning air with altitude, and the curvature of the Earth on the range of the super cannon.

Construct Your Own Problem Consider a ball tossed over a fence. Construct a problem in which you calculate the ball’s needed initial velocity to just clear the fence. Among the things to determine are; the height of the fence, the distance to the fence from the point of release of the ball, and the height at which the ball is released. You should also consider whether it is possible to choose the initial speed for the ball and just calculate the angle at which it is thrown. Also examine the possibility of multiple solutions given the distances and heights you have chosen.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Cc test coll. OpenStax CNX. Dec 15, 2015 Download for free at http://legacy.cnx.org/content/col11717/1.4
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