Final answer:
The combined velocity of the sports car and pickup truck after the collision is 20.2 m/s, obtained using the conservation of linear momentum.
Step-by-step explanation:
To calculate the velocity of the two vehicles that will move off together after the collision, we can use the principle of conservation of linear momentum. The momentum before the collision for the sports car and the pick-up truck can be found using the formula momentum (p) = mass (m) × velocity (v).
For the sports car: p_car = 800.0 kg × 13.0 m/s = 10400 kg·m/s
For the pick-up truck: p_truck = 1200 kg × 25.0 m/s = 30000 kg·m/s
The total momentum before the collision is the sum of moments of the two vehicles, which is p_total = p_car + p_truck = 10400 kg·m/s + 30000 kg·m/s = 40400 kg·m/s.
After the collision, since the car and the truck lock together, their combined mass is m_combined = 800.0 kg + 1200 kg = 2000 kg.
To find the combined velocity, we use the conservation of momentum:
p_total = m_combined × v_combined
40400 kg·m/s = 2000 kg × v_combined
Now we solve for v_combined:
v_combined = 40400 kg·m/s / 2000 kg = 20.2 m/s.
This is the velocity at which the locked vehicles will move off together after the collision.