A homeowner uses a snowblower to clear his driveway. Knowing that the snow is discharged at an average angle of 40° with the horizontal, determine the initial velocity ν0 of the snow.

Question

A homeowner uses a snowblower to clear his driveway. Knowing that the snow is discharged at an average angle of 40° with the horizontal, determine the initial velocity [latex]{ u }_{ 0 }[/latex] of the snow.

Accepted Answer

First note

[latex]\begin{aligned}& \left( u_x ight)_0= u_0 \cos 40^{\circ} \& \left( u_y ight)_0= u_0 \sin 40^{\circ}\end{aligned}[/latex]

Horizontal motion. (Uniform)

[latex]x=0+\left( u_x ight)_0 t[/latex]

At B: [latex]\quad \quad \quad 14=\left( u_0 \cos 40^{\circ} ight) t \quad ext { or } \quad t_B=\frac{14}{ u_0 \cos 40^{\circ}}[/latex]

Vertical motion. (Uniformly accelerated motion)

[latex]y=0+\left( u_y ight)_0 t-\frac{1}{2} g t^2 \quad\left(g=32.2 \ ext{ft} / s ^2 ight)[/latex]

At B: [latex]\quad \quad \quad 1.5=\left( u_0 \sin 40^{\circ} ight) t_B-\frac{1}{2} g t_B^2[/latex]

Substituting for [latex]t_B[/latex]

[latex]1.5=\left( u_0 \sin 40^{\circ} ight)\left\lgroup\frac{14}{ u_0 \cos 40^{\circ}} ight group-\frac{1}{2} g\left\lgroup\frac{14}{ u_0 \cos 40^{\circ}} ight group^2[/latex]

or [latex]\quad \quad \quad u_0^2=\frac{\frac{1}{2}(32.2)(196) / \cos ^2 40^{\circ}}{-1.5+14 an 40^{\circ}}[/latex]

or [latex]\quad \quad \quad \quad \quad \quad u_0=22.9 \ ext{ft} / s \blacktriangleleft[/latex]

Question 11.105: A homeowner uses a snowblower to clear his driveway. Knowin...

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