Question

Trig based physics problem:

Euron fires a 15 kg bolt due West with a speed of 20 m/s from a scorpion (a big crossbow) at one of Daenery's dragons that is flying near the ground and moving due North with a speed of 5 m/s. The dragon has a mass of 200 kg. The bolt strikes the dragon and remains embedded in the dragons hide.

a) Calculate the final magnitude and direction of the velocity of the dragon and bolt.

b) Show that this collision is inelastic by calculating the loss in the kinetic energy due to the collision.

Answer 1

here,

mass of bolt , m1 = 15 kg

mass of dragon , m2 = 200 kg

initial speed of bolt , u1 = - 20 i m/s

initial speed of dragon , u2 = 5 j

let the final speed be v

using conservation of momentum

m1 * u1 + m2 * u2 = (m1 + m2) * v

15 * (-20 i) + 200 * (5j) = (15 + 200) * v

v = ( - 1.4 i m/s + 4.65 j m/s)

a)

the final magnitude of velocity , |v| = sqrt(1.4^2 + 4.65^2) = 4.86 m/s

the direction of velocity , theta = arctan(4.65/1.4) = 73.2 degree North of West

b)

the initial kinetic energy , KEi = 0.5 * m1 * u1^2 + 0.5 * m2 * u2^2

KEi = 0.5 * 15 * 20^2 + 0.5 * 200 * 5^2 J = 5500 J

the final kinetic energy , KEf = 0.5 * (m1 + m2) * v^2

KEf = 0.5 * ( 200 + 15) * 4.68^2 = 2355 J

as KEf is not equal to KEi

the collison is inelastic