Question

Two cars collide in an intersection. The speed limit in that zone is 30 mph. The car (mass of 1250 kg) was going 17.4 m/s (38.9 mph) the truck (2020 kg) t boned the car in the middle of the intersection. The car was slowed down to only 6.7 m/s. The truck after colliding with the car was going 10.3 m/s. How fast did the truck go into the intersection?

Answer 1

u₂ = 3.7 m/s

Step-by-step explanation:

Here, we use the law of conservation of momentum, as follows:

`m_1u_1+m_2u_2=m_1v_1+m_2v_2\\`

where,

m₁ = mass of the car = 1250 kg

m₂ = mass of the truck = 2020 kg

u₁ = initial speed of the car before collision = 17.4 m/s

u₂ = initial speed of the tuck before collision = ?

v₁ = final speed of the car after collision = 6.7 m/s

v₂ = final speed of the truck after collision = 10.3 m/s

Therefore,

`(1250\ kg)(17.4\ m/s)+(2020\ kg)(u_2)=(1250\ kg)(6.7\ m/s)+(2020\ kg)(10.3\ m/s)\\\\(2020\ kg)(u_2) = 8375\ N.s + 20806\ N.s - 21750\ N.s\\\\u_2=(7431\ N.s)/(2020\ kg)`

u₂ = 3.7 m/s