Determine the speed a2500-kg pick-up truck should attain

Zyrill Maravilla

Zyrill Maravilla

Answered question

2022-05-13

Determine the speed a2500-kg pick-up truck should attain for it to have (a) the same momentum as a 20,000-kg bus travelling at 90-kph (b) the same kinetic energy as a 1800-kg car travelling at 100-kph

Answer & Explanation

Nick Camelot

Nick Camelot

Skilled2023-05-07Added 164 answers

We are given a series of problems to solve related to momentum and kinetic energy.
(a) We need to determine the speed at which a 2500-kg pick-up truck should travel to have the same momentum as a 20,000-kg bus travelling at 90 km/h.
The momentum of an object is given by the product of its mass and velocity: p=mv.
The momentum of the bus is:
pbus=mv=(20,000 kg)(25 m/s)=500,000 kg m/s.
To have the same momentum, the pick-up truck must also have a momentum of 500,000 kg m/s. Let vtruck be the velocity of the pick-up truck. Then:
ptruck=mvtruck=(2500 kg)(vtruck)=500,000 kg m/s.
Solving for vtruck, we get:
vtruck=500,000 kg m/s2500 kg=200 m/s.
(b) We need to determine the speed at which a 2500-kg pick-up truck should travel to have the same kinetic energy as a 1800-kg car travelling at 100 km/h.
The kinetic energy of an object is given by the formula: K=12mv2.
The kinetic energy of the car is:
Kcar=12mv2=12(1800 kg)(100 km/h3.6 m/s)2=625,000 J.
To have the same kinetic energy, the pick-up truck must also have a kinetic energy of 625,000 J. Let vtruck be the velocity of the pick-up truck. Then:
Ktruck=12mvtruck2=12(2500 kg)(vtruck)2=625,000 J.
Solving for vtruck, we get:
vtruck=2Ktruckm=2(625,000 J)2500 kg=50 m/s.

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