# 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

2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
50 N... (50 *1.732)N
Sahim
Plz cheak the ans and give reply..
Sahim
Is earth is an inertial frame?
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
Sahim
thanks
Irungu
Most welcome
Sahim
Hey.. I've a question.
Is earth inertia frame?
Sahim
only the center
Shii
What is an abucus?
Irungu
what would be the correct interrogation "what is time?" or "how much has your watch ticked?"
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Young's modulus = stress/strain strain = extension/length (x/l) stress = force/area (F/A) stress/strain is F l/A x
El
so solve it
Ebenezer
Ebenezer
two bodies x and y start from rest and move with uniform acceleration of a and 4a respectively. if the bodies cover the same distance in terms of tx and ty what is the ratio of tx to ty
what is cesium atoms?
The atoms which form the element Cesium are known as Cesium atoms.
Naman
A material that combines with and removes trace gases from vacuum tubes.
Shankar
what is difference between entropy and heat capacity
Varun
Heat capacity can be defined as the amount of thermal energy required to warm the sample by 1°C. entropy is the disorder of the system. heat capacity is high when the disorder is high.
Chathu
I want learn physics
sir how to understanding clearly
Vinodhini
try to imagine everything you study in 3d
revolutionary
pls give me one title
Vinodhini
displacement acceleration how understand
Vinodhini
vernier caliper usage practically
Vinodhini
karthik sir is there
Vinodhini
what are the solution to all the exercise..?
What is realm
The quantum realm, also called the quantum scale, is a term of art inphysics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−9meters) or less or at very low temperature.
revolutionary
How to understand physics
i like physics very much
Vinodhini
i want know physics practically where used in daily life
Vinodhini
I want to teach physics very interesting to studentd
Vinodhini
how can you build interest in physics
Prince
Austin
understanding difficult
Vinodhini
vinodhini mam, physics is used in our day to day life in all events..... everything happening around us can be explained in the base of physics..... saying simple stories happening in our daily life and relating it to physics and questioning students about how or why its happening like that can make
revolutionary
revolutionary
anything send about physics daily life
Vinodhini
How to understand easily
Vinodhini
revolutionary
even when you see this message in your phone...it works accord to a physics principle. you touch screen works based on physics, your internet works based on physics, etc....... check out google and search for it
revolutionary
what is mean by Newtonian principle of Relativity? definition and explanation with example
what is art physics
I've been trying to download a good and comprehensive textbook for physics, pls can somebody help me out?
Olanrewaju
try COLLEGE PHYSICS!! I think it will give you an edge.
Lawal
smith
This may seem like a really stupid question, but is mechanical energy the same as potential energy? If not, what is the difference?
what is c=1\c1,c=2\c2,c=3\c3
Akinbulejo
mechanical energy is of two types 1: kinetic energy 2: potential energy,so, potential energy is actually the type of mechanical energy ,the mechanical due to position is designated as potential energy
Iram
Thank you!!!!!
Nikki
Can someone possibly walk me through this problem? " A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgehammer. The hammer hits the spike with a speed of 65.0 m/s. If one-third Of the hammer's kinetic energy is converted to the internal energy of rhe hammer and spike.
Nikki
how much does the total internal energy increase
Nikki
you know the mass and the velocity of the hammer. therefore using the equation (mv^2)/2 you can find the kinetic energy. then take one third of this value and that will be your change in internal energy. here, the important thing is that spike is stationary so it does not contribute to initial Energ
Chathu
Thabk you! :)
Nikki
what is the formula for finding the to total capacitance in series arrangement
Don't know
Ugwu
C = 1/C1+1/C2+1/C3
Nangbun
c=1/c1+1/c2+1/c3
Akinbulejo