91影视

Newton鈥檚 laws of motion show the relationship between the moving particle or object鈥檚 displacement, initial and final velocity, acceleration, and time.

The velocity contains two components, one is a horizontal component and another one is a vertical.

According to Newton鈥檚 laws of motion,

$\mathrm{s}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2$

Here, s, u, a, and t are displacement, initial velocity, time, and acceleration respectively.

Horizontal distance traveled by the ball, ${\mathrm{s}}_{\mathrm{Hb}}=188\mathrm{m}$

Angle, $\mathrm{胃}={45}^{\mathrm{o}}$

Height of the ball,${\mathrm{s}}_{\mathrm{v}}=0.9\mathrm{m}$

Height of the fence, $\mathrm{h}=3.0\mathrm{m}$

Acceleration due to gravity, $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$

The horizontal distance of the fence, ${\mathrm{s}}_{\mathrm{Hf}}=116\mathrm{m}$

For the horizontal motion the gravity is zero. Therefore,

$\begin{array}{rcl}{\mathrm{s}}_{\mathrm{Hb}}& =& \mathrm{耻迟肠辞蝉胃}+\frac{1}{2}{\mathrm{gt}}^2\\ & =& \mathrm{耻迟肠辞蝉胃}+0\end{array}$

$\begin{array}{rcl}\mathrm{t}& =& \frac{{\mathrm{s}}_{\mathrm{Hb}}}{\mathrm{耻肠辞蝉胃}}\\ & =& \frac{188\mathrm{m}}{\mathrm{ucos}{45}^{\mathrm{o}}}\end{array}$

For the vertical motion, gravity is negative. Therefore, the equation of motion will becomes,

$\begin{array}{rcl}{\mathrm{s}}_{\mathrm{v}}& =& \mathrm{耻蝉颈苍胃迟}-\frac{1}{2}{\mathrm{gt}}^2\\ -0.9\mathrm{m}& =& \mathrm{u}\sin {45}^{\mathrm{o}}\left(\frac{188\mathrm{m}}{\mathrm{u}\cos {45}^{\mathrm{o}}}\right)-\frac{1}{2}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right){\left(\frac{188\mathrm{m}}{\mathrm{u}\cos {45}^{\mathrm{o}}}\right)}^2\\ -0.9\mathrm{m}& =& 188\mathrm{m}-\left(\frac{3.4647脳{10}^5}{{\mathrm{u}}^2}\right)\\ 187.1& =& \frac{3.4647脳{10}^5}{{\mathrm{u}}^2}\\ {\mathrm{u}}^2& =& 0.185脳{10}^4\\ \mathrm{u}& =& 43.0\mathrm{m}/\mathrm{s}\end{array}$

Hence, the initial velocity is 43.0 m/s.

For the horizontal motion, gravity is zero

$\begin{array}{rcl}{\mathrm{s}}_{\mathrm{Hf}}& =& \mathrm{耻肠辞蝉胃}脳\mathrm{t}+\frac{1}{2}{\mathrm{gt}}^2\\ & =& \mathrm{ucos}{45}^{\mathrm{o}}脳\mathrm{t}+0\end{array}$

$\begin{array}{rcl}\mathrm{t}& =& \frac{{\mathrm{s}}_{\mathrm{Hf}}}{\mathrm{u}\cos {45}^{\mathrm{o}}}\\ & =& \frac{116\mathrm{m}}{43.0\mathrm{m}/\mathrm{s}脳0.707}\\ & =& 3.82\mathrm{s}\end{array}$

For the vertical motion, gravity is negative

$\begin{array}{rcl}\mathrm{s}& =& \mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2\\ & =& 30.3\mathrm{m}/\mathrm{s}脳3.82\mathrm{s}+\frac{1}{2}脳\left(-9.8\mathrm{m}/{\mathrm{s}}^2\right)脳{\left(3.83\mathrm{s}\right)}^2\\ & =& 115.746\mathrm{m}-71.878\mathrm{m}\\ & =& 43.87\mathrm{m}\end{array}$

Hence, the height of ball is 0.90 m and the height of fence is 3.0 m . Now the height of the ball above the fence will be,

$43.87\mathrm{m}+0.90\mathrm{m}-3.0\mathrm{m}=41.768\mathrm{m}$