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A freely falling body from a tower of height h covers a distance h/2 in the last second of its motion. The height of the tower is nearly 1]58m 2]50m 3]60m 4]55m

A freely falling body from a tower of height h covers a distance h/2 in the last second of its motion. The height of the tower is nearly
1]58m
2]50m
3]60m
4]55m

Grade:11

3 Answers

Piyush Kumar Behera
417 Points
7 years ago
see in this type of problems use the following approach...

we alreaady know that =  S = U + a/2(2N-1) [ WHERE U = INITIAL SPEED , & N = value of TIME IN Tth SECOND . ]

so using the formula ------

h/2 = u + a/2(2t-1)

h/10 = 2t-1 { u=0 & a=10}

t = h+10/20

so, total time = h+10/20

now by formula = h=ut + 1/2at^2, (u=0 a=10)

h=h^2+100+20h/80

on solving - h = 58.28 metres.

if you are really helped then please approve

 

Manoj Dixit
29 Points
7 years ago
let h distance be covered in t seconds then h/2 distance is covered in t-1 seconds
first using the formula of distance covered in nth second we get
h/2 = 0 + 10/2(2t-1)     { u=0 a=10 }
on solving this we get 
h = 20t-10     equation 1
we know 
s = ut + at2/2
here u = 0 a = 10 s = h
h = 5t2   puttting this in equation 1 we get 
5t2 = 20t -10
t2 – 4t + 2
on solving this equation we get 
t = 2 \displaystyle \displaystyle \pm 21/2 
we will choose 2 - 2½
the answer would be very small hence according to the options we will choose               t = 2 + 21/2
we have already seen that h= 5t2
putting the value of t we get 
h = 30 + 20*2½
putting 21/2 = 1.4 we get h = 30 + 28 = 58 
hence the answer is 58
please approve 
 
 
Ankit Jaiswal
165 Points
7 years ago
Hi Hermonie,
                     I think this might help
let h distance be covered in t seconds then h/2 distance is covered in t-1 seconds
first using the formula of distance covered in nth second we get
h/2 = 0 + 10/2(2t-1)     { u=0 a=10 }
on solving this we get 
h = 20t-10     equation 1
we know 
s = ut + at2/2
here u = 0 a = 10 s = h
h = 5t2   puttting this in equation 1 we get 
5t2 = 20t -10
t2 – 4t + 2
on solving this equation we get 
t = 2 \displaystyle \displaystyle \pm 21/2 
we will choose 2 - 2½
the answer would be very small hence according to the options we will choose               t = 2 + 21/2
we have already seen that h= 5t2
putting the value of t we get 
h = 30 + 20*2½
putting 21/2 = 1.4 we get h = 30 + 28 = 58 
hence the answer is 58
please approve and any doubt freely
 

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