A 1300 kg car is approaching the hill shown in the figure at 13.0 m/s when it su

Question

A 1300 kg car is approaching the hill shown in the figure at 13.0 m/s when it suddenly runs out of gas.(Figure 1) What is the car's speed after coasting down the other side?

Question 2: As a 15000 kg jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60000 N/m.If the spring stretches 30 m to stop the plane, what was the plane's landing speed?

Question 3: A 1300 kg sports car accelerates from 0m/s to 30m/s in 10 s. What is the average power of the engine?

Explanation / Answer

Here ,
let the final speed of the car is v m/s

Using conservation of energy

0.5 * m v^2 = 0.5 * m * u^2 + m * g * h

0.5 * v^2 = 0.5 * 13^2 + 9.8 * 5

solving for v

v = 16.34 m/s

the final speed of the car is 16.34 m/s

2)

let the initial speed of the plane is v m/s

Using conservation of energy

0.5 * m * v^2 = 0.5 * k * x^2

0.5 * 15000 * v^2 = 0.5 * 60000 * 30^2

v = 60 m/s

the landing speed of plane is 60 m/s

3)

let the power is P

average power = net work done /time

average power = change in kinetic energy /time

average power = 0.5 * 1300 * (30^2 - 0)/10

average power = 58500 W

the average power is 58500 W

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