1) Work is defined as the energy transferred to an object by the application of constant force, and is found by multiplying the force in Newtons (5500) by the distance the object moves in meters (50). So we calculate `5500 xx 50=275,000` Joules.
2) Gravity exerts a constant force on the hiker found by multiplying the mass of the hiker (55.6 kg) by the gravity acceleration (9.8 `m//s^2` ) and we get a gravity force of 544.88N. Since the hiker ascends 50m upward, gravity does negative work found by `544.88 xx -50=-27,244` Joules
3) Since work is energy being transferred to an object by application of a constant force, it is reasonable to assume that the cart will have a kinetic energy equal to the work done on the cart. The work done on the cart is found by `W=200N xx 10 m=2000J` So the cart has 2000J kinetic energy.
4) The car starts, already having kinetic energy. The car's Kinetic energy (K) can be found with the following formula `K=1/2mv^2` The car's mass (m) is 1208kg, and starting velocity (`v_1`)is 10 m/s so the Car's starting kinetic energy is `1/2(1208)(10)^2=6.04 xx 10^2` Joules. Then, `4.00 xx 10^5` more joules of work is done giving the car an additional `4.00 xx 10^5` Joules of Kinetic energy. So the car has a final kinetic energy of `4.604 xx10^5` Joules. We plug that and the car's mass into the formula for kinetic energy and solve for v to find the car's final velocity `460400=1/2(1208)v^2=604v^2`
`->460400/604=v^2->v=sqrt(460400/604)~~27.61` m/s. The car ends with a velocity of 27.61 m/s