Question

A blue car with mass mc = 539 kg is moving east with a speed of vc = 15 m/s and collides with a purple truck with mass mt = 1300 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of ? = 52

Answer 1

m_c = 539 kg

m_t = 1300 kg

V_cxi = 15 m/s = initial velocity of car in X-direction (east)      going east.

V_txi= initial velocity of truck in X-direction (east) = 0

V_cyi = initial velocity of car in Y-direction (south) = 0

V_tyi = initial velocity of truck in Y-direction (south)?

V = final velocity

V_fx = final velocity along X-direction = V Cos52

V_fy= final velocity along Y-direction = V Sin52

1) initial momentum of car = m_c V_cxi = 539 x 15 = 8085 kgm/s

2) using conservation of momentum along the x-direction ::

m_c V_cxi + m_t V_txi = (m_c + m_t) V_fx

539 x 15 + 1300 x 0 = (539 + 1300) V cos52

8085 = 1132.2 V

V = 7.14 m/s

So V_fy= V sin52 = 7.14 Sin52 = 5.63 m/s

using conservation of momentum along the y-direction ::

m_c V_cyi + m_t V_tyi = (m_c + m_t) V_fy

539 x 0 + 1300 x V_tyi = (539 + 1300) (5.63 m/s)

V_tyi = 7.96 m/s

initial momentum of truck = m_t V_tyi= 1300 x 7.96 = 10348 kgm/s

3) speed of truck before collision = V_tyi = 7.96 m/s

4) final momentum of combination = (m_c + m_t) V = (1300 + 539) 7.14 = 13130.5 kgm/s

5) V = 7.14 m/s