The height of the ramp is 9 meter
<u>Solution:</u>
It is given that a skateboard ramp is 15 meters long and it extends 12 meters from the base of the starting point.
If we look at the sum, closely we understand that the ramp is a right angled triangle.
Which has a base length of 12 metres and a hypotenuse of 15 metres.
We need to find its height.
To do so we can use the Pythagoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition, we get
Since we already know the lengths of the hypotenuse and base we can substitute them in the formula and solve for the height.
Let height of the ramp be denoted by ‘h’
Therefore, the height of the ramp is 9 meter
<span>Acceleration of a passenger is centripetal acceleration, since the Ferris wheel is assumed at uniform speed:
a = omega^2*r
omega and r in terms of given data:
omega = 2*Pi/T
r = d/2
Thus:
a = 2*Pi^2*d/T^2
What forces cause this acceleration for the passenger, at either top or bottom?
At top (acceleration is downward):
Weight (m*g): downward
Normal force (Ntop): upward
Thus Newton's 2nd law reads:
m*g - Ntop = m*a
At top (acceleration is upward):
Weight (m*g): downward
Normal force (Nbottom): upward
Thus Newton's 2nd law reads:
Nbottom - m*g = m*a
Solve for normal forces in both cases. Normal force is apparent weight, the weight that the passenger thinks is her weight when measuring by any method in the gondola reference frame:
Ntop = m*(g - a)
Nbottom = m*(g + a)
Substitute a:
Ntop = m*(g - 2*Pi^2*d/T^2)
Nbottom = m*(g + 2*Pi^2*d/T^2)
We are interested in the ratio of weight (gondola reference frame weight to weight when on the ground):
Ntop/(m*g) = m*(g - 2*Pi^2*d/T^2)/(m*g)
Nbottom/(m*g) = m*(g + 2*Pi^2*d/T^2)/(m*g)
Simplify:
Ntop/(m*g) = 1 - 2*Pi^2*d/(g*T^2)
Nbottom/(m*g) = 1 + 2*Pi^2*d/(g*T^2)
Data:
d:=22 m; T:=12.5 sec; g:=9.8 N/kg;
Results:
Ntop/(m*g) = 71.64%...she feels "light"
Nbottom/(m*g) = 128.4%...she feels "heavy"</span>
the answer is either A or B, probably C, maybe D. I know it's one of those
Answer:
4986 ounces/m³
Step-by-step explanation:
1 kilogram = 35.274 ounces
1 cubic foot = 0.0283 cubic metre
We are converting kg/ft³ to ounces/m³
Hence:
4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³
= 4985.7243816 ounces/m³
Approximately to the nearest whole number = 4986 ounces/m³
