<< Chapter < Page Chapter >> Page >

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

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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.
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply
Practice Key Terms 7

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Cc test coll. OpenStax CNX. Dec 15, 2015 Download for free at http://legacy.cnx.org/content/col11717/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Cc test coll' conversation and receive update notifications?