A body of mass 'm' drops from Bridge into the water of the river. The bridge is 10m high from the water's surface. (a). Find the speed of the body 5m above the water surface. 
(b). Find the speed of the body before it strikes the water. 
((a) 9.9 m s⁻¹ (b) 14 m s⁻¹)


Given:

Mass of body = m 
Height of the bridge from the water surface = h1 = 10 m 

Data for option (a) 
Height at velocity is to be found = h2 = 5 m 
Effective height through witch the body fall = h = h1 - h2 = 10 m - 5 m = 5 m
Value of g = 9.81 m s⁻²

Data for option (b) 
Effective height through witch the body fall = h = h1 = 10 m
Value of g = 9.81 m s⁻²

To Find:

(a).  Speed of the body 5m above the water surface = v = ? 
(b). Speed of the body before it strikes the water = v = ?  

Solution:

According to the law of conservation of energy

Gain in K.E = Loss in P.E.

`\ frac{1}{2}`mv² = mgh

v² = 2gh

v = `\ sqrt {2gh}` --------------- (1)


(a).  To find speed of the body 5m above the water surface.

Using equation (1)

v = `\ sqrt {2gh}`

by putting values (h = 5 m)

v = `\ sqrt {2ｘ9.81 m s⁻²ï½˜ 5 m}`

v = `\ sqrt {98.1 m² s⁻²}`

v = 9.904 m s⁻¹

or

v = 9.9 m s⁻¹ ----------------Ans.


(b). To find the speed of the body before it strikes the water. 


Using equation (1)

v = `\ sqrt {2gh}` 

by putting values (h = 10 m)

v = `\ sqrt {2ｘ9.81 m s⁻²ï½˜ 10 m}`

v = `\ sqrt {196.2 m² s⁻²}`

v = 14.007 m s⁻¹

or

v = 14 m s⁻¹ ----------------Ans.


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