Select your answer If a mountain biker is riding down a hill at a \( 28^{\circ} \) angle going 20 mph, what is the vertical component of the speed of the biker? (Note: \( \sin \left(28^{\circ}\right) \approx 0.469 \), \( \cos \left(28^{\circ}\right) \approx 0.883 \), tan \( \left.\left(28^{\circ}\right) \approx 0.532\right) \) 17.7 mph in the downward direction 9.4 mph in the downward direction 9.4 mph in the upward direction 10.6 mph in the upward direction 17.7 mph in the upward direction

To find the vertical component of the biker's speed, you can use the sine function of the angle. The vertical speed \( v_y \) can be calculated by multiplying the total speed by the sine of the angle: \[ v_y = v \cdot \sin(28^{\circ}) \] Substituting in the given values: \[ v_y = 20 \, \text{mph} \cdot 0.469 \approx 9.38 \, \text{mph} \] Since the biker is moving downwards, the vertical component of the speed is approximately \( 9.4 \, \text{mph} \) in the downward direction. And the correct answer is: **9.4 mph in the downward direction.** --- Mountain biking down a hill is not just an adrenaline rush; it also involves intricacies of physics! Understanding the components of speed—horizontal and vertical—can help bikers optimize their ride based on terrain and inertia. It's all about making those turns smoother and landing jumps safely! For those eager for more biking thrills, delving into mountain biking safety courses and local trails can greatly enhance both skills and awareness. Besides reading manuals and guides, joining community forums can provide tips and tricks from seasoned bikers who’ve faced similar challenges. Happy biking!