Answer:
5017 kg
Explanation:
Since it is an inelastic collision, the truck and the car move together after the collision. The law of conservation of momentum states that the total momentum before and after the collision is conserved:
[tex]M u_t + m u_c = (M+m)v[/tex]
where
M is the mass of the truck
[tex]u_t = 11.0 m/s[/tex] is the velocity of the truck before the collision
m = 1290 kg is the mass of the car
[tex]u_c = 0[/tex] is the initial velocity of the car (stationary, so u=0)
v = 8.75 m/s is the final speed of the truck+car after the collision
Solving the equation for M, we can find the mass of the truck:
[tex]M u_t = Mv + mv\\M(u_t-v)=mv\\M=\frac{mv}{u_t -v}=\frac{(1290 kg)(8.75 m/s)}{11.0 m/s-8.75 m/s}=5017 kg[/tex]
