Question

A ship is approaching a cliff of height 105 m above sea level. A gun fitted on the ship can fire shots with
a speed of 110 ms-'. Find the maximum distance from the foot of the cliff from where the gun can hit an
object on the top of the cliff. ​

Answer 1

Explanation:

1100 m is the maximum

distance from the foot of the

cliff from where the gun can hit an object on the top of the

cliff

Explanation:

Let say angle = a and time = t to reach

peak

S = ut + (1/2)at?

=> 105 = 110 Sina *t - 5t?

=> 110 Sina *t = 105 + 5t2

Squaring both sides => (110Sina)?t? 1052 25t*

1050t? => (1102 - (110Cosa))t? = 1052 + 25t* + 1050t?

=

+

+

=> (110Cosa)? t? = 110?t? - 105? - 25t* -

1050t?

=> (110Cosa)? t? =- 25t* + 11050t? - 1052

Horizontal Distance

D = 110Cosa * t

Z=D2 = (110Cosa)? t? => Z = - 25t4 + 11050t2 - 1052

as D is + ve hence D will be maximum if D2 =

Z is maximum

Z = - 25t4 + 11050t- 1052 Let substitute t2 = x

=> Z =- 25x2 + 11050x - 1052 dZ/dx = -50x + 11050

=> x = 11050/50

=> x = 221

d?Z/dx? = - 50 Hence maximum value

t? = 221 =>t = v221

D2 = Z = - 25t4 + 11050t? 1052 = -25(221)2 + 11050(221) - 1052 = -12,21,025 + 24,42,050 - 11025

= 12,10,0004

=> D = 1100 m

maximum distance from the foot of the cliff

from where the gun can hit an object on the

top of the cliff. = 1100 m

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