91Ó°ÊÓ

Firstly, the known variables need to be identified from the problem. Here, the horizontal distance (d_x) is given as \(108 \mathrm{~m}\), the vertical distance (d_y) is \(55.0 \mathrm{~m}\) and the angle of projection, \(\theta\), is \(10.0^{\circ}\) below the horizontal.

To facilitate our calculations, the negative angle of projection can be converted to an equivalent positive angle by subtracting it from \(180^{\circ}\). Therefore, the equivalent positive angle becomes \(180^{\circ} - 10.0^{\circ} = 170^{\circ}\). It is important also to convert this angle into radians since most trigonometric calculations assume radian measure. Conversion formula: \(\text{Rad} = \frac{\text{Degrees} \times \pi}{180}\), hence, \(\theta = \frac{170 \times \pi}{180} = 2.967 \mathrm{~rad}\).

In projectile motion, the horizontal and vertical motions are independent of each other except for the time of flight, which is common to both. Taking the horizontal motion into consideration, the formula relates the horizontal distance to the launch speed and the angle of projection \(d_x = v_0 \times t \times \cos{\theta}\). From the vertical motion, \(d_y = v_0 \times t \times \sin{\theta} - \frac{1}{2} g t^2\), where \(g\) is the acceleration due to gravity. From these two equations, eliminating the time \(t\) gives us the formula for initial launch speed \(v_0\): \(v_0 = \sqrt{\frac{d_x^2}{\cos^2{\theta}} + \frac{2 d_y g}{\sin{\theta}}}\), and plugging the known values of \(d_x\), \(d_y\), \(g\) (taking \(9.81 \mathrm{~m/s^2}\) as the acceleration due to gravity), and \(\theta\) will yield the initial launch speed.

The statement in (b) could be explained based on the principles of aerodynamics. Nordic skiers streamline their bodies and skis to minimize air resistance, also the skis provide certain lift, these factors can reduce the energy required for the jump. In real-world physics, we cannot ignore these factors completely.