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three points object A,B and C are projected at the projection of theta1,theta2,theta3 respectively.if all of them attain same maximum height,show that their time of flight are also identical

three points object A,B and C are projected at the projection of theta1,theta2,theta3 respectively.if all of them attain same maximum height,show that their time of flight are also identical

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
From The Newton’s motion eqns. 
let the heights be:
ha=u12sin2q1/2g
hb= u22sin2q2/2g
hc= u32sin2q3/2g

ha=hb=hc=h (GIVEN)

t1,t2,t3 are the time required by A,B and C to complete the motion.

t1=2u1sinq1/g
=>t12=4u12sin2q1/g

Mathematically by the formula above,
ha+t12=1+3t12/2
ha=1+t12/2

Similarly, hb=1+t22/2
hc=1+t32/2

as ha=hb=hc
=>1+t12/2=1+t22/2=1+t32/2
=>t1=t2=t3
Hnece Proved.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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