The relevant equation to use here is:
y = v0 t + 0.5 g t^2
where y is the vertical distance, v0 is initial velocity =
0, t is time, g = 9.8 m/s^2
y = 0 + 0.5 * 9.8 * 3^2
<span>y = 44.1 meters</span>
Answer:
Explanation:
It means that you only need apply 1/4th of the actual force required to operate the lever as you have an mechanical advantage which permits you to do 4 times the work with the same amount of effort.
The speed of the falcon is 144 km/h
Explanation:
The speed of a body is a scalar quantity telling how fast the object is moving, without giving any information about its direction.
It can be calculated as:
where
d is the distance covered
t is the time taken
In this problem, the falcon has a speed of
We want to convert it into km/h. Let's keep in mind that:
1 km = 1000 m
1 h = 3600 s
Therefore, we convert as follows:
Learn more about speed:
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To find the tangent plane to the surface f(x,y,z)=0 at a point (X,Y,Z) we use the following method:
<span>Calculate grad f = (f_x, f_y, f_z). The normal vector to the surface at the point (X,Y,Z) is grad f(X,Y,Z). The equation of a plane with normal vector n which passes through the point p is (r-p).n=0, where r=(x,y,z) is the position vector. So the equation of the tangent plane to the surface through the point (X,Y,Z) is ((x,y,z)-(X,Y,Z)).grad f(X,Y,Z)=0. </span>
<span>Now in your case we have f(x,y,z)=y-x^2-z^2, so grad f=(-2x,1,-2z), and the equation of the tangent plane at the point (X,Y,Z) is </span>
<span>((x,y,z)-(X,Y,Z)).(-2X,1,-2Z)=0, </span>
<span>that is </span>
<span>-2X(x-X)+1(y-Y)-2Z(z-Z)=0, </span>
<span>i.e. </span>
<span>-2Xx+y-2Zz = -2X^2+Y-2Z^2. (1) </span>
<span>Now compare this equation with the plane </span>
<span>x + 2y + 3z = 1. (2) </span>
<span>The two planes a_1x+b_1y+c_1z=d_1, a_2x+b_2y+c_2z=d_2 are parallel when (a_1,b_1,c_1) is a multiple of (a_2,b_2,c_2). So the two planes (1),(2) are parallel when (-2X,1,-2Z) is a multiple of (1,2,3), and we have </span>
<span>(-2X,1,-2Z)=1/2(1,2,3) </span>
<span>for X=-1/4 and Z=-3/4. On the paraboloid the corresponding y coordinate is Y=X^2+Z^2=1^4+9^4=5/2. </span>
<span>So the tangent plane to the given paraboloid at the point (-1/4,5/2,-3/4) is parallel to the given plane.</span>
