Respuesta :
Answer:
The distance close to the peak is 597.4 m.
Explanation:
Given that,
Distance of the first ship from the mountain [tex]d=2.46\times10^{3}\ m[/tex]
Height of island[tex]h=1.80\times10^{3}\ m[/tex]
Distance of the enemy ship from the mountain [tex]d'=6.10\times10^{2}\ m[/tex]
Initial velocity [tex]v=2.55\times10^{2}\ m/s[/tex]
Angle = 74.9°
We need to calculate the horizontal component of initial velocity
Using formula of horizontal component
[tex]v_{x}=v\cos\theta[/tex]
Put the value into the formula
[tex]v_{x}=2.55\times10^{2}\cos74.9[/tex]
[tex]v_{x}=66.42\ m/s[/tex]
We need to calculate the vertical component of initial velocity
Using formula of vertical component
[tex]v_{y}=v\sin\theta[/tex]
Put the value into the formula
[tex]v_{y}=2.55\times10^{2}\sin74.9[/tex]
[tex]v_{y}=246.19\ m/s[/tex]
We need to calculate the time
Using formula of time
[tex]t=\dfrac{d}{v_{x}}[/tex]
[tex]t=\dfrac{2.46\times10^{3}}{66.42}[/tex]
[tex]t=37.03\ sec[/tex]
We need to calculate the height of the shell on reaching the mountain
Using equation of motion
[tex]H= v_{y}t-\dfrac{1}{2}gt^2[/tex]
Put the value in the equation
[tex]H=246.19\times37.03-\dfrac{1}{2}\times9.8\times(37.03)^2[/tex]
[tex]H=2397.4\ m[/tex]
We need to calculate the distance close to the peak
Using formula of distance
[tex]H'=H-h[/tex]
Put the value into the formula
[tex]H'=2397.4-1800[/tex]
[tex]H'=597.4\ m[/tex]
Hence, The distance close to the peak is 597.4 m.
