Question

A 2,700 kg truck is moving east at 14 m/s when it collides head-on with a 1,800 kg SUV going west. After the collision, the two vehicles stick together and have an initial velocity of 2.23 m/s immediately after the collision. The suv driver claims that he was travelling below the 15 m/sspeed limit before the collision. Determine whether the driver is telling the truth.

Answer 1

he was not telling the true

Explanation

Step 1

Diagram

An elastic collision is a collision where both the Kinetic Energy, KE, and momentum, p are conserved. In other words

$\frac{1}{2}m_1v^2_i+\frac{1}{2}mv^2_2=\frac{1}{2}(m_1+m_2)v^2_3$

then, Let

$\begin{gathered} m1=2700\text{ kg} \\ v1=14\text{ m/s} \\ m2=1800\text{ Kg} \\ v_2=x \\ v3=2.23 \end{gathered}$

now, replace

$\begin{gathered} \frac{1}{2}m_1v^2_i+\frac{1}{2}mv^2_2=\frac{1}{2}(m_1+m_2)v^2_3 \\ \frac{1}{2}(2700)(14^2)+\frac{1}{2}(1800)x^2=(2700+1800)\cdot(2.23)^2 \\ 264600+900x^2=22378.05 \\ +900x^2=22378.05-264600 \\ 900x^2=\frac{242221.95}{900} \\ x^2=269.1355 \\ x=16.40 \\ x=16.40\text{ m/s} \end{gathered}$

so, the velocity of the driver 2 was

16.40 meters per second, therefore

he was not telling the true