Question

1. A 26 kg cannon ball is fired from a cannon with muzzle speed of 962 m/s at an angle of 19.2 ◦ with the horizontal. The acceleration of gravity is 9.8 m/s 2 . Use conservation of mechanical energy to find the maximum height reached by first ball. Answer in units of m.2. A second identical ball is fired at an angle of 144◦ . What is the total mechanical energy at the maximum height of the second ball. Answer in units of J.

Answer 1

given,

Mass of the cannon ball = 26 Kg

speed of cannon with muzzle = 962 m/s

angle with horizontal = 19.2°

angle of second ball = 144°

for first ball

`v_y = v sin \theta_h`................(1)

`v_y = (962) sin 19.2^0`

`v_y = 316.37\ m/s`

now equating kinetic energy and potential energy

`(1)/(2)mv_y^2 = mgh`

`(1)/(2)v_y^2 = gh`

`h = (v_y^2)/(2g)`.................(2)

`h = (316.37^2)/(2* 9.8)`

h = 5106.63 m

total mechanical energy of ball at maximum height

angle = 144° = (90° + 54°)

so θ = 54°

`E = (1)/(2)m(vsin\theta)^2`

`E =(1)/(2)* 26 * (962* sin 54^0)^2`

E = 7.75 x 10⁶ J