Question

A snow-covered ski slope makes an angle of $35.0°$with the horizontal. When a ski jumper plummets onto the hill, a parcel of splashed snow is thrown up to a maximum displacement of $1.50mat16.0°$from the vertical in the uphill direction as shown in Figure P3.28. Find the components of its maximum displacement (a) parallel to the surface and (b) perpendicular to the surface.

Short answer

1. The component is parallel to the surface $=-1.17m$.
2. The component is perpendicular to the surface$=0.944m$.

Step-by-step solution

Define parallel to the surface and perpendicular to the surface.

• If any normal to one is normal to the other, two surfaces are said to be parallel; it can then be proven that the distance between two locations with a common normal is a constant, known as the parallelism constant.
• If a line is perpendicular to every line in the plane it intersects, it is said to be perpendicular to the plane. This concept is dependent on how perpendicularity between lines is defined.

(a) Determine the component parallel to the surface.

Note that the x-axis should be parallel to the slope and the y-axis should be perpendicular to it. The component that is parallel to the surface.

$$\begin{gathered} =(1.5)\times cos\left(90°+35°+16°\right) \\ =-1.17m \end{gathered}$$

Hence, the component parallel to the surface$=-1.17m$ .

(b) Determine the component perpendicular to the surface.

Perpendicular to the surface component.

$$\begin{gathered} =(1.5)\times sin\left(90°+35°+16°\right) \\ =0.944m \end{gathered}$$

Hence, the component perpendicular to the surface$=0.944m$