Tossing A Ball

I throw a ball up in the air with some initial velocity v 1 v_1 and it stays in the air for some time t 1 t_1 . I then throw the ball straight up with velocity v 2 v_2 and find that this time it stays in the air for a time t 2 = 2 t 1 t_2=2t_1 . What is v 2 / v 1 v_2/v_1 ?


The answer is 2.

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19 solutions

Rahma Anggraeni
May 4, 2014

The formula for vertical motion up is v t = v 0 g t v_{t} = v_{0}-gt

Since the v t v_{t} is 0 , so the formula becomes v 0 = g t \boxed{v_{0}=gt}

v 1 = g t 1 v_{1}=gt_{1}

Then..

v 2 = g t 2 v_{2}=gt_{2}

v 2 = 2 g t 1 v_{2}=2gt_{1}

So..

v 2 v 1 = 2 g t 1 g t 1 \frac{v_{2}}{v_{1}}=\frac{2gt_{1}}{gt_{1}}

v 2 v 1 = 2 1 = 2 \frac{v_{2}}{v_{1}}=\frac{2}{1}= \boxed{2}

Zakaria Sellami
May 8, 2014

We have x = g 2 t 2 + v 0 t x=-\frac{g}{2}t^2+v_0t (Assuming the ball is thrown from x = 0 x=0 ) . When the balls gets back to the ground: x = 0 x=0 (with t 0 t \neq 0 ) then, v 1 = g 2 t 1 v_1=-\frac{g}{2}t_1 and v 2 = g 2 t 2 = g t 1 v_2=-\frac{g}{2}t_2=-gt_1 .
v 2 v 1 = g t 1 g 2 t 1 = 2 \dfrac{v_2}{v_1} = \dfrac{-gt_1}{-\dfrac{g}{2}t_1}=2 .

Isabella Sealey
May 3, 2014

v = u + a t v=u+at

Given that acceleration due to gravity is the same for the two throws, we know that v t v\propto t . This means that if you double t t , you also double v v .

Since t 2 = 2 × t 1 { t }_{ 2 }=2\times { t }_{ 1 } ,

v 2 = 2 × v 1 { v }_{ 2 }=2\times { v }_{ 1 }

v 2 v 1 = 2 \therefore \frac { { v }_{ 2 } }{ { v }_{ 1 } } =2

V=u-gt where u=0unit and g is constant !!

Muhammad Kamal
Mar 8, 2014

a formula for this case is:

t = s/v

t = time s = distance v = velocity

from above formula, we can take a conclude that if t is become twice bigger than before, then v is become a half of before.

Aravind Raj
Mar 2, 2014

for 1st ball 0=V1-gt1 V1=gt1

for 2nd ball 0=V2-gt2 V2=gt2

V2/V1=t2/t1=2

Shubham Sharma
Jan 20, 2014

s=ut+at^{2}/2 s=o we get v=gt/2 hence v2 /v1=t2/t1 =2

Avisek Agarwal
Jan 19, 2014

If time taken for second ball is half as time taken for first ball then the speed of second ball should be twice as first ball ,

So speed of first ball be anything but it is half as second ball ,

So let the speed of first ball be 1(v1) then the speed for second ball equals to 2 (v2) ,

2(v2) / 1 (v1) = 2..

Rakesh Kirtania
Jan 15, 2014

final velocity(v)=0 unit, v=v(1)-g t(1)...................(1) v=v(2)-g t(2)...................(2) 2/1 then,answer will be 2

Noorish Saboor
Jan 14, 2014

when the ball moves up with velocity vi and when it is thrown 2nd time it moves up with velocity v2.the first ball takes time t and 2nd ball takes time t2 which is double so it means its velocity is also double .when we take any number instead of velocity its answer is always 2 like this v2/v1 when we take v2=10 and v1=5 because v2 is double that of v1 then 10/5 becomes equal to 2

yours one is the best answer

Mikku Thomas - 7 years, 2 months ago
Janaky Murthy
Jan 10, 2014

for 1st ball 0=v1-gt1 v1=gt1

for 2nd ball 0=v2-gt2 v2=gt2

v2/v1=t2/t1=2

Avirook Roy
Jan 6, 2014

velocity 1st case is (at) in 2nd case is (2at) dividing 2nd by 1st =2.

Sathish Kumar
Dec 27, 2013

as t2=2t1 => v2/v1=2t1/t1 => v2/v1=2

Ibrahim Hamim
Dec 26, 2013

u can solve it through......v=u-gt

Budi Utomo
Dec 23, 2013

v2/v1 = t2/t1 ---> v2/v1 = 2t1/t1 = 2 [m/s]. Answer : 2

Khaja Zubair
Dec 22, 2013

as we know that this comes under time of ascent so V=-GT V1=-9.81 T(T=T1) V2=-9.81 2T(T2=2T1) V2/V1=-9.81 T/-9.81 2T V2/V1=2

Well,the time and speed are directly proportionals,so if the T2 = 2xT1,we have the conclusion that V2 = 2xV1, so , 2/1 = 2.

Pradeep Gb
Dec 17, 2013

for both cases final velocity ie V(f) will be equal to zero for the case 1 V(f)=v1 -gt 0=v1-gt for the case 2 v(f)=v2-g t1 0=v2-2g t1 v1/v2=2

Rugved Dhore
Dec 15, 2013

v=u+at. In this case u is 0, thus, v=at thus v is directly proportinal to time. so,T2=2T1. So v2=2V1 v2/v1=2

how u is 0 in this case ?

Devesh Rai - 7 years, 5 months ago

plz see the question...it stays in d air..so that the final velocity u=0

Bharath P - 7 years, 5 months ago

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