Question

75 kg missile is dropped downwards from an air plane, and has a speed of 60 m/s at an altitude of 850 m above the ground. Determine: 

(a) The K.E. possessed by the missile at 850 m. 

(b) The P.E. possessed by the missile at 850 m. 

(c) The total mechanical energy possessed by the missile. 

(d) The K.E. and velocity with which it strikes the ground.

Answer 1

(a) Given: 

Mass of the missile, m = 75 kg and Speed, v = 60 m/s 

Therefore, K.E. = 1/ 2 mv² = 1 /2 × 75 × 60 × 60 = 13500 J

(b) Given, 

Mass of the missile, m = 75 kg 

Acceleration due to gravity, g = 10 m/s² and Height, h = 850 m 

Therefore, P.E. = m × g × h = 75 × 10 × 850 = 637500 J 

(c) Total mechanical energy of the missile = K.E. + P.E. 

= 135000 + 637500 = 7.7 × 10⁵J

(d) K.E. at the ground = 7.7 × 10⁵J 

K.E. = 1 /2 mv² ,       Therefore, v² = 2 K.E. / m

Velocity with which missile strikes the ground =143.2 m/s