A motorcyclist is trying to leap across a canyon by driving horizontally off a cliff (height= 60 m) at a speed of 25 m/s. The cycle strikes a cliff on the other side (height= 30 m) at a speed of 15 m/s. Find the work done by air resistance.
To find the work done by air resistance, we first need to determine the change in kinetic energy of the motorcyclist.
The change in kinetic energy (ΔKE) can be calculated as the difference between the initial kinetic energy (KEi) and the final kinetic energy (KEf). The initial kinetic energy is given by:
KEi = (1/2) * m * v^2
where m is the mass of the motorcyclist and v is their initial velocity.
Given that the speed of the motorcyclist is 25 m/s, we can substitute the values into the equation:
KEi = (1/2) * m * (25)^2
Similarly, we can calculate the final kinetic energy using the final velocity:
KEf = (1/2) * m * (15)^2
Now, the work done by air resistance (W_air) can be found by subtracting the final kinetic energy from the initial kinetic energy:
W_air = KEi - KEf
Substituting the previously calculated values:
W_air = (1/2) * m * (25)^2 - (1/2) * m * (15)^2
Simplifying this expression, we find the work done by air resistance.