Scampering mouse

A mouse runs 3 m 3~\mbox{m} east and 4 m 4~\mbox{m} north in 5 seconds 5~\mbox{seconds} . What is the magnitude of the mouse's average velocity during its run in m/s ?


The answer is 1.

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11 solutions

Daniel Chiu
Dec 8, 2013

Since east and north are perpendicular, the mouse runs 3 2 + 4 2 = 25 = 5 \sqrt{3^2+4^2}=\sqrt{25}=5 meters. Since velocity is d i s t a n c e t i m e \dfrac{distance}{time} , the average velocity is 5 m e t e r s 5 s e c o n d s = 1 m s \dfrac{5\ meters}{5\ seconds}=\boxed{1}\dfrac{m}{s}

VELOCITY related with displacement and given by phythagoras thm and devided by the given time.

vilas joshi - 7 years, 6 months ago

y we use phythagoras theorem?

shivangi srivastava - 7 years, 6 months ago

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We must find the net displacement, a vector quantity like velocity, rather than distance, which is a scalar.

EDIT: misread

Daniel Chiu - 7 years, 6 months ago

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Because he can't walk in two direction. So phythagoras.

Ewerton Cassiano - 7 years, 6 months ago

thanks daniel

Arrii Kamal - 7 years, 6 months ago

Too easy don't do this

Mardokay Mosazghi - 7 years, 2 months ago

In order to solve this problem, we need to find out the distance covered by the mouse. As it runs 3 3 m eaat and 4 4 m, the total distance covered by it can be found by using Pythagoras theorem. he runs a total of 3 2 + 4 2 \sqrt{3^{2}+4^{2}} = 9 + 16 =\sqrt{9+16} = 25 =\sqrt{25} = 5 m =5 m So, the magnitude of the mouse's average velocity = D i s p l a c e m e n t T i m e =\frac{Displacement}{Time} = 5 5 =\frac{5}{5} = 1 m s 1 =\boxed{1 ms^{-1}}

Pham Tung
Dec 9, 2013

Use Pythagore 's law : x = \sqrt{3^2 + 4^2 } = 5 (m ) v =\frac {s}{t} = \frac {5}{5} = 1

Ashish Menon
May 28, 2016

The length covered by the mouse = 3 2 + 4 2 = 5 \sqrt{3^2 + 4^2} = 5 . So, the average velocity = 5 5 = 1 m / s \dfrac{5}{5} = \color{#69047E}{\boxed{1}}m/s .

Ng Lin Shun
Dec 13, 2013

As velocity is a vector quantity,so,its formula is displacement/time.Displacement is the shortest distance between two points in a specific direction,so according to pythogoras theorem,the displacement between two points is 5.Thus ,the velocity is 5/5=1

Karthik Rk
Dec 12, 2013

Average=3+4/2=3.5 Time given=5s To find Magnitude=average/time(s) Magnitude=3.5/5s=0.7 nearly equal to 1=1ans

by phythagoras theorem,you will get s=hypotenuse,where s^2=3^2 + 4^2,s=5m,

then by applying v=s/t=5m/5s=1m/s...

Shreya Shukla
Dec 10, 2013

the net displacement of the mouse is sqrt( 3sqr + 4sqr ) = 5 metres the time taken is 5 seconds. thus velocity of mouse is 5m/5s= 1 m/s

Xongro Klan
Dec 10, 2013

H² = c'² + c"² \* H² = 3²+4² \* H=5m \* v=s/t \* v= 5\5 \* v=1

Arun Chouhan
Dec 10, 2013

net displacement=sqrt( 3^2+4^2)=5 . avg velocity = total displacement/total time= 5/5=1 m/s.

Shubham Thakkar
Dec 9, 2013

The mouse forms two sides of a right-angled triangle as it goes 3 m east and then forming a right-angle, turns to go 4 m north. Now, velocity = Displacement/time Hence the displacement = Average distance which can also be shown as the hypotenuse of the right - angled triangle formed. Hypotenuse = (By Pythagoras theorem) Square root of (3^2 + 5^2) which happens to be = 5 Hence, Displacement = 5 m and Time taken = 5 s (Given) So, velocity = 5/5 = 1

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