Answer:
Length = 50m
Width = 31.84m
Step-by-step explanation:
Perimeter of a track = 200m
The perimeter of a track with two semi-circular end and two rectangular regions = P
Perimeter of a semi-circle = ½(2πr)
Length of a rectangle = x
Perimeter of the rectangle = x+x
P = ½(2πr) + ½(2πr)+x + x
P = 2πr + 2x
200 =2πr + 2x
2πr = 200 – 2x
2πr = 2(100 – x)
r = 2(100 – x) / 2π
r = (100-x)/π
total area of the rectangular region =A
A= x(2r)
= (x)2[(100-x)/π]
= 2x[(100-x)/π]
A = (200x – 2x^2)/π
Differentiate A with respect to x
dA/dx = (200 -4x)/π
at critical point, first derivative vanishes(dA/dx = 0)
(200 -4x)/π = 0
-4x =-200
x =-200/-4
x = 50
this means length (x) = 50m
put x=50 into r = (100-x)/π
r= (100-50)/π
r =50/π
width = 2r
width = 2(50/π)
= 2(19.62)
= 31.84m
Answer:
Step-by-step explanation:
La energía mecánica total está dada por:
En donde:
m: es la masa = 150 g
v: es la velocidad = 0.8 m/s
h: es la altura = 25 m
g: es la gravedad = 9.81 m/s²
Por lo tanto, la energía mecánica total es 36.84 J.
Espero que te sea de utilidad!