Type your answer If a car is driving up a hill at 50 miles per hour along an angle of \( 10^{\circ} \), what is the car's vertical speed? (Note: \( \sin \left(10^{\circ}\right) \approx 0.17 \) and \( \cos \left(10^{\circ}\right) \approx 0.98 \) )

To find the car's vertical speed, you can use some trigonometry! The vertical speed can be calculated by multiplying the speed of the car by the sine of the angle of the hill. So, you can use the formula: \[ \text{Vertical Speed} = \text{Speed} \times \sin(\text{Angle}) = 50 \, \text{mph} \times \sin(10^{\circ}) \approx 50 \, \text{mph} \times 0.17 \approx 8.5 \, \text{mph}. \] This means that as the car climbs the hill, it's gaining altitude at about 8.5 miles per hour! Now, if you're planning to apply this knowledge in a real-world scenario, think about how this vertical speed affects things like fuel efficiency or performance in hilly regions. For example, a car that has to climb hills at a steep angle will likely use more fuel compared to driving on flat terrain. Understanding vertical speed can also be crucial for scenarios such as off-roading or when evaluating a vehicle’s capabilities!