# 3.5 Addition of velocities  (Page 6/12)

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Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.50 m/s, and the second a velocity of 4.20 m/s. (a) What is the velocity of the second runner relative to the first? (b) If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity? (c) What distance ahead will the winner be when she crosses the finish line?

(a) 0.70 m/s faster

(b) Second runner wins

(c) 4.17 m

Verify that the coin dropped by the airline passenger in the [link] travels 144 m horizontally while falling 1.50 m in the frame of reference of the Earth.

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. The ball is thrown at an angle of $25.0º$ relative to the ground and is caught at the same height as it is released. What is the initial velocity of the ball relative to the quarterback ?

$17\text{.}\text{0 m/s}$ , $\text{22}\text{.}1º$

A ship sets sail from Rotterdam, The Netherlands, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction $\text{40.0º}$ north of east. What is the velocity of the ship relative to the Earth?

(a) A jet airplane flying from Darwin, Australia, has an air speed of 260 m/s in a direction $5.0º$ south of west. It is in the jet stream, which is blowing at 35.0 m/s in a direction $15º$ south of east. What is the velocity of the airplane relative to the Earth? (b) Discuss whether your answers are consistent with your expectations for the effect of the wind on the plane’s path.

(a) $2\text{30 m/s}$ , $8.0º$ south of west

(b) The wind should make the plane travel slower and more to the south, which is what was calculated.

(a) In what direction would the ship in [link] have to travel in order to have a velocity straight north relative to the Earth, assuming its speed relative to the water remains $7\text{.}\text{00 m/s}$ ? (b) What would its speed be relative to the Earth?

(a) Another airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction $\text{20º}$ south of east (as in [link] ). Its direction of motion relative to the Earth is $45.0º$ south of west, while its direction of travel relative to the air is $5.00º$ south of west. What is the airplane’s speed relative to the air mass? (b) What is the airplane’s speed relative to the Earth?

(a) 63.5 m/s

(b) 29.6 m/s

A sandal is dropped from the top of a 15.0-m-high mast on a ship moving at 1.75 m/s due south. Calculate the velocity of the sandal when it hits the deck of the ship: (a) relative to the ship and (b) relative to a stationary observer on shore. (c) Discuss how the answers give a consistent result for the position at which the sandal hits the deck.

The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of 2.20 m/s in a direction $30.0º$ east of north relative to the Earth. It encounters a wind that has a velocity of 4.50 m/s in a direction of $50.0º$ south of west relative to the Earth. What is the velocity of the wind relative to the water?

$6\text{.}\text{68 m/s}$ , $\text{53}\text{.}3º$ south of west

A ball is thrown vertically upwards so that its max height is 100m...at the same instant another ball is dropped frm 100m above the ground...where will the two balls meet and why?
50m
wenhe
why?
Blessing
Blessing
😟
Blessing
75m
S.M
how?😨
Blessing
because they approach each other at different speeds, but same acceleration, so you can calculate its height above ground.
S.M
Yeah. He's right. Your question seems very similar to a question I did in physics class, and our answer was 50.so yeah that's why I said that. But 75m is correct
wenhe
what's is waves
Waves is the disturbance of a medium such that the particles in the medium vibrate to cause the movement of energy from one point to another without the the particle itself moving.
Prince
what is the medium that light waves travel through?
Luke
and electrons, protons, neutrons and quarks for that matter?
Luke
it's spacetime that light and every other particles travel through actually
S.M
ether
Anand
for above question, i think 50m is the correct answer. the first ball will behave exactly like 2nd ball when it reaches 100m (max height).
James
From rest, a body moves with an acceleration of 8m/s in 10 secs. calculate the distance during the 8th seconds
Caleb
please use energy conservation to solve this problem. i think i have an answer but it is too long to explain here.
James
one is with some initial velocity v, while other one will start it's journey from rest, so they can't travel equal distance in equal amount of time
S.M
to be honest I knew the answer was just pointing out a flaw in above answer and light does not require a medium to travel through, this was proved in the 1887 by Michelson and Morley.
Luke
the two balls have different acceleration. the accelerations are same in magnitude but in different directions for them. so the first ball will gradually move slower and the 2nd ball will move faster.
James
u can just put 50m or 75m in equation to check whether right or not
James
the total energy of the two balls are equal, KE + PE. 1/2mv(1)^ 2 + mgh(1) = 1/2mv(2)^2 +mgh(2). use that
James
Give an example (but not one from the text) of a device used to measure time and identify what change in that device indicates a change in time.
hour glass, pendulum clock, atomic clock?
S.M
tnks
David
A heart pumping blood would indicate a change in time as its volume or pressure changed. The ratio of displacement or change in configuration between any 2 systems can indicate time.
Khashon
how did they solve for "t" after getting 67.6=.5(Voy + 0)t
Find the following for path D in [link] : (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.
the topic is kinematics
David
can i get notes of solid state physics
Lohitha
just check the chpt. 13 kinetic theory of matter it's there
David
is acceleration a fundamental unit.
no it is derived
Abdul
no
Nisha
K thanks
David
no it's not its derived
Emmanuel
hi
Hello
Emmanuel
hello
David
Hello Emmanuel
Emmanuel
I'm good
that's good
Emmanuel
how are you too
am cool
Emmanuel
spending time summarizing
Emmanuel
Emmanuel
I am fin
Longwar
ok
hi guys can you teach me how to solve a logarithm?
how about a conceptual framework can you simplify for me? needed please
Villaflor
Hello what happens when electrone stops its rotation around its nucleus if it possible how
Afzal
I think they are constantly moving
Villaflor
yep what is problem you are stuck into context?
S.M
not possible to fix electron position in space,
S.M
Physics
Beatriz
yes of course Villa flor
David
equations of kinematics for constant acceleration
A bottle full of water weighs 45g when full of mercury,it weighs 360g.if the empty bottle weighs 20g.calculate the relative density of mercury and the density of mercury....pls I need help
well You know the density of water is 1000kg/m^3.And formula for density is density=mass/volume Then we must calculate volume of bottle and mass of mercury: Volume of bottle is (45-20)/1000000=1/40000 mass of mercury is:(360-20)/1000 kg density of mercury:(340/1000):1/50000=(340•40000):1000=13600
Sobirjon
the latter is true
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture...take density of water as 1g/cm3 and density of liquid 1.2g/cm3
Lila
plz hu can explain Heisenberg's uncertainty principle
who can help me with my problem about acceleration?
ok
Nicholas
how to solve this... a car is heading north then smoothly made a westward turn during the travel the speed of the car remains constant at 1.5km/h what is the acceleration of the car? the total travel time of the car as it smoothly changed its direction is 15 minutes
Vann
i think the acceleration is 0 since the car does not change its speed unless there are other conditions
Ben
yes I have to agree, the key phrase is, "the speed of the car remains constant...," all other information is not needed to conclude that acceleration remains at 0 during the entire time
Luis
who can help me with a relative density question
Lila
1cm3 sample of tin lead alloy has mass 8.5g.the relative density of tin is 7.3 and that of lead is 11.3.calculate the percentage by weight of tin in the alloy. assuming that there is no change of volume when the metals formed the alloy
Lila
So it looks like you need a formula for rotational acceleration. Are you asking about its angular acceleration?
Khashon
morning, what will happen to the volume of an ice block when heat is added from -200°c to 0°c... Will it volume increase or decrease?
no
Emmanuel
hi what is physical education?
Kate
BPED..is my course.
Kate
No
Emmanuel
I think it is neither decreases nor increases ,it remains in the same volume because of its crystal structure
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture. take density of water as 1g/cm3 and density of liquid as 1.2g/cm3
Lila
Sorry what does it means"no changes in volume occured"?
Sobirjon
volume can be the amount of space occupied by an object. But when an object does not change in shape it will still occupy the same space. Thats why the volume will still remain the same
Ben
Most soilds expand when heated but if it changes state at 0C it will have less volume. Ice floats because it is less dense ie a larger mass per unit volume.
Richard
how to calculate velocity
v=d/t
Emeka
Villaflor
Villaflor
v=d/t
Nisha
hello bro hw is life with you
Mine is good. How about you?
Chase
Hi room of engineers
yes,hi sir
Okwethu
hello
akinmeji
Hello
Mishael
hello
Jerry
hi
Sakhi
hi
H.C
so, what is going on here
akinmeji
Ajayi
good morning ppl
ABDUL
If someone has not studied Mathematics enough yet, should theu study it first then study Phusics or Study Basics of Physics whilst srudying Math as well?
whether u studied maths or not, it is advisable to start from d basics cuz it is essential to know dem
Nuru
yea you are right
wow, you got this w/o knowing math
Thomas
I guess that's it
Thomas
later people
Thomas
mathematics is everywhere
Anand
thanks but dat doesn't mean it is good without maths @Riaz....... Maths is essential in sciences particularly wen it comes to PHYSICS but PHYSICS must be started from the basic which may also help in ur mathematical ability
Nuru
A hydrometer of mass 0.15kg and uniform cross sectional area of 0.0025m2 displaced in water of density 1000kg/m3.what depth will the hydrometer sink
Lila
16.66 meters?
Darshik
16.71m2
aways
,i have a question of let me give answer
aways
the mass is stretched a distance of 8cm and held what is the potential energy? quick answer
aways