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QUESTION

Mar 31, 2025

Data: Acceleration due to gravity at Earth’s surface = 9.8 m/s2 1. A car traveling at a certain speed knocks down a cyclist. The driver of the car claims that he was traveling below the speed limi

Data: Acceleration due to gravity at Earth’s surface = 9.8 m/s2

1. A car traveling at a certain speed knocks down a cyclist. The driver of the car claims that he was traveling below the speed limit of S km/h. Police measured the skid marks made by the car at D m long. It is known that the maximum deceleration for this type of car is A m/s2.

(a) Derive an equation to determine whether the car was traveling above or below the speed limit.

(b) Derive an equation to find the time taken to bring the car to rest. State assumptions made to answer (a) and (b).

2. Modern cars have crumple-zones which are designed to increase the stopping time and stopping distance of the car so that the average force exerted on the occupants is reduced, provided the occupants have on seat belts and the airbags work. The front crumple-zone is 1.00 m long and collapses completely in a head-on crash at 55.0 km/h. A working airbag stops an occupant moving in 0.38 s.

(a) Find the car’s deceleration and stopping time.

(b) Find the average force on a 90.0-kg passenger who has on a seat belt but his airbag fails to open.

(d) Who is more likely to be severely injured? Why?

3. A 2,000-kg spacecraft traveling at 8,000 m/s in outer space accelerates by burning 20 kg of rocket fuel, which is ejected from the engine at an exhaust velocity of 4,500 m/s relative to the rocket. The procedure took 4 seconds.

(a) Accounting for the mass of fuel ejected, calculate the velocity of the spacecraft once the fuel is burned. (b) Find the total kinetic energy of the spacecraft-fuel system (i) before the fuel burn and (ii) after the fuel burn. Account for the energy difference in (i) and (ii).