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

SUV driver was driving just over the limit at 15.425 m/s

Step-by-step explanation:

Using conservation of momentum:

2700 (14 ) = momentum 1 = 37800

-1800 x = momentum 2 these summed =

(2700+1800) (2.23) = final momentum

2700(14 ) - 1800x = (2700+1800)(2.23)

solving for x = 15.425 m/s = SUV speed

Answer 2

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

`(1)/(2)m_1v^2_i+(1)/(2)mv^2_2=(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} (1)/(2)m_1v^2_i+(1)/(2)mv^2_2=(1)/(2)(m_1+m_2)v^2_3 \\ (1)/(2)(2700)(14^2)+(1)/(2)(1800)x^2=(2700+1800)\cdot(2.23)^2 \\ 264600+900x^2=22378.05 \\ +900x^2=22378.05-264600 \\ 900x^2=(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