Final answer:
To determine the velocity of the safari jeep after the collision with a signpost using conservation of momentum, the jeep's post-collision velocity is found to be approximately 34.3 m/s.
Step-by-step explanation:
The given problem can be solved using the principle of conservation of linear momentum. This principle states that when no external forces act on a system of objects, the total momentum of the system remains constant. In the case of the safari jeep and the signpost, the situation is an inelastic collision because after the collision, the signpost is stuck to the jeep. To solve the mathematical problem completely, we use the formula:
Initial momentum of the system = Final momentum of the system,
Momentum of the jeep before collision + Momentum of the signpost before collision = Momentum of the combined system after collision.
So,
(m_jeep * v_jeep) + (m_signpost * v_signpost) = (m_combined * v_combined)
Given the initial velocity (v_signpost) of the signpost is 0 (since it was stationary), the formula simplifies to:
(6887 kg * 34.4 m/s) + (16.8 kg * 0 m/s) = (6887 kg + 16.8 kg) * v_combined
By performing the multiplication and then dividing both sides by the combined mass, we can find the velocity of the jeep after the collision:
v_combined = (6887 kg * 34.4 m/s) / (6887 kg + 16.8 kg)
After carrying out the calculations, we get:
v_combined ≈ 34.3 m/s
Therefore, the velocity of the safari jeep after colliding with the signpost and having it stuck on is approximately 34.3 m/s.