A 90.0 kg person is running up some stairs at 0.500 m/s. If the staircase is angled at 45.0° to the horizontal, then the power needed to run up the stairs is
A) 312 Watts.
B) 395 Watts.
C) 302 Watts.
D) 275 Watts.
E) 441 Watts.

Question

Quizplus · Accepted Answer

The power needed to run up the stairs can be calculated using the formula $P = \frac{W}{t}$, where $W$ is the work done and $t$ is the time. Since the person is moving against gravity, $W = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $h$ is the height gained. The velocity given is along the stairs, so to find the vertical component (which gives us $h/t$), we use $v_y = v \sin(\theta)$, where $\theta = 45^\circ$. Thus, $v_y = 0.500 \times \sin(45^\circ) = 0.500 \times 0.707 = 0.354$ m/s. The power is then $P = mgv_y = 90.0 \times 9.8 \times 0.354 = 312$ Watts.

A 900 Kg Person Is Running Up Some Stairs at 0