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A vertically projected body reaches half of the maximum height at time 't'. At what time will reach the maximum height ? Choose the answer from the given options.

A vertically projected body reaches half of the maximum height at time 't'. At what time will reach the maximum height ?
Choose the answer from the given options.

Question Image
Grade:11

2 Answers

Himanshu Rathour
119 Points
2 years ago
Let the maximum height be H and time to reach maximum height be T
H/2=ut²-1/2gt²........(i)
H=uT²-1/2gT²......(ii)
=> 4ut-2gt²=2uT-gT²
2gt²-4ut+2uT-gT²=0
Now,this is quadratic equation in terms of t
t=
 
Himanshu Rathour
119 Points
2 years ago
t=(4u+{16u²116guT+8g²T²})/4g...... (iii) 
Now 
By, v=u+at
u=gT.    {at max height v=0}
Putting value of u in equation (iii)
t=(1+1/√2)T
T=√2/(√2+1)
Hence answer is 2

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