motion in a plane

Question 1

projectile motion

Accepted Answer

y=xtan(theta)-(1/2)g^2cos^2(theta) =xtan(theta)*(1-(x/R)) =ax-bx^2 , a=tan(theta), b=g/2u^2cos^2(theta) ,a=R ,a^2/4b=H

Question 2

H and R relationship

Accepted Answer

4H=Rtan(theta)

Question 3

velocity at any time during the motion

Accepted Answer

vnet=√(u^2+g^2t^2-2ugtsin(theta)) tan(alpha) =usin(theta)-gtcos(theta)

Question 4

for same range equations

Accepted Answer

T1/T2=tan(theta) ,H1/H2=tan^2(theta) T1×T2=2R , H1×H2=R^2/16 , T1^2+T2^2=4Rmax ,H1+H2=Rmax/2

Question 5

net displacement

Accepted Answer

r,=√(x^2+y^2) x=ucos(theta)t y=usin(theta)t-(1/2)gt^2

Question 6

momentum at any time

Accepted Answer

pi=m(ucos(theta))i^+m(usin(theta))j^pf=m(ucos(theta))i^+m(usin(theta)-gt)j^ at maximum height ∆p=-musin(theta)j^

Question 7

horizontal projectile

Accepted Answer

x=ut y=1/2gt^2 y=(1/2)g x^2^2

Question 8

time of flight in horizontal projectile

Accepted Answer

T=√(2H)

Question 9

v in horizontal projectile

Accepted Answer

v=√((u^2)+(gt)^2) v=u/cos(alpha) alpha is angle b/w horizontal and resultant velocity

Question 10

number of steps

Accepted Answer

n=2u^2hb^2

Question 11

wmin whour and wmin/whour =?

Accepted Answer

wmin =2π/(60×60) whour=2π/(12×60×60) wmin/whour=12

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