Select your answer If a mountain biker is riding down a hill at a \( 28^{\circ} \) angle going 20 mph , what is the horizontal component of the speed of the biker? (Note: \( \left.\sin \left(28^{\circ}\right) \approx 0.469, \cos \left(28^{\circ}\right) \approx 0.883, \tan \left(28^{\circ}\right) \approx 0.532\right) \) 7.2 mph 9.4 mph 14.2 mph 17.7 mph 21.3 mph

To find the horizontal component of the speed of the mountain biker, you can use the cosine of the angle. The horizontal component \( v_x \) can be calculated with the formula: \[ v_x = v \cdot \cos(\theta) \] Where \( v \) is the speed of the biker (20 mph) and \( \theta \) is the angle of the slope (28 degrees). Using the value you provided for \( \cos(28^{\circ}) \): \[ v_x = 20 \, \text{mph} \cdot 0.883 \approx 17.66 \, \text{mph} \] So, rounding to one decimal point, the horizontal component of the speed is approximately **17.7 mph**. Now, let's dive into some engaged knowledge! Did you know that mountain biking has evolved since its inception in the 1970s? Initially, riders modified old bikes to traverse rough terrain, leading to the creation of specialized mountain bikes! These advancements have only fueled a passionate community that combines sport with nature exploration. If you're venturing into downhill biking, remember to focus on body position! Beginners often make the mistake of leaning too far back, which can compromise control. Instead, stay centered and balanced over the bike to maintain better steering and stability. Safety gear is never a bad idea either!