Question

The cannon was fired only once with a charge of 100 kilograms of gunpowder. It is said that the projectile fired from it made a small lake in Chaksu which is about 35 km from Jaipur.

(i) The barrel is cylindrical in shape and made up of iron with density 7.8×103 kg/m3 . Its length, outer diameter and inner diameter are 6.15m, 0.7m & 0.35m respectively. Calculate

(a) mass of the iron used to construct the barrel.
(b) maximum volume of explosive that can be fitted in the cannon. (c) Assuming the given data to be correct calculate the density of the explosive and compare with that of density of water (= 1000 kg/m3 ).

(ii) Assume that the Jaivaan barrel is mounted horizontally 1000m above the ground level and the fired projectile lands on the ground at 14.14 km. Calculate the velocity of the projectile.

Answer 1

Given : Jaivaan barrel is mounted horizontally 1000m above the ground level and the fired projectile lands on the ground at 14.14 km.

To Find : Calculate the velocity of the projectile.

Solution:

Height = 1000 m

initial vertical velocity = 0

S = ut + (1/2)at²

=> 1000  = 0 + (1/2)9.8t²

=> t² = 1000/4.9

=> t² = 10000/49

=> t = 100/7   sec

Horizontal Distance = 14.14 km  = 14140 m

time = 100/7   sec

Horizontal Velocity =  14140  / (100/7)

= 989.8 m/s

velocity of the projectile. = 989.8 m/s

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