Questions: Wanda runs up a hill that makes an angle of 15.5 degrees above the horizontal. The hypotenuse of the hill is 221 meters long. If Wanda has a mass of 72 kg and she does this in 131 seconds, how many horsepower does she generate? 0.59 hsp 0.64 hsp 0.51 hsp 0.43 hsp

Solution Steps

To find the vertical height \( h \) of the hill, we use the sine function: \[ h = 221 \sin(15.5^\circ) \] Using a calculator: \[ h \approx 221 \times 0.2672 \approx 59.0552 \text{ meters} \]

The work done \( W \) by Wanda is given by: \[ W = mgh \] where \( m = 72 \) kg, \( g = 9.81 \) m/s\(^2\), and \( h = 59.0552 \) meters. Substituting these values: \[ W = 72 \times 9.81 \times 59.0552 \approx 41700 \text{ joules} \]

Power \( P \) is the work done divided by the time \( t \): \[ P = \frac{W}{t} = \frac{41700}{131} \approx 318.3206 \text{ watts} \]

1 horsepower (hsp) is equal to 745.7 watts. Therefore, the power in horsepower is: \[ \text{Power in hsp} = \frac{318.3206}{745.7} \approx 0.4268 \text{ hsp} \]

Final Answer