Answer:
3.28 m
3.28 s
Explanation:
We can adopt a system of reference with an axis along the incline, the origin being at the position of the girl and the positive X axis going up slope.
Then we know that the ball is subject to a constant acceleration of 0.25*g (2.45 m/s^2) pointing down slope. Since the acceleration is constant we can use the equation for constant acceleration:
X(t) = X0 + V0 * t + 1/2 * a * t^2
X0 = 0
V0 = 4 m/s
a = -2.45 m/s^2 (because the acceleration is down slope)
Then:
X(t) = 4*t - 1.22*t^2
And the equation for speed is:
V(t) = V0 + a * t
V(t) = 4 - 2.45 * t
If we equate this to zero we can find the moment where it stops and begins rolling down, that will be the highest point:
0 = 4 - 2.45 * t
4 = 2.45 * t
t = 1.63 s
Replacing that time on the position equation:
X(1.63) = 4 * 1.63 - 1.22 * 1.63^2 = 3.28 m
To find the time it will take to return we equate the position equation to zero:
0 = 4 * t - 1.22 * t^2
Since this is a quadratic equation it will have to answers, one will be the moment the ball was released (t = 0), the other will eb the moment when it returns:
0 = t * (4 - 1.22*t)
t1 = 0
0 = 4 - 1.22*t2
1.22 * t2 = 4
t2 = 3.28 s
Answer:
6.5 kW
Explanation:
Input power = 20 kW = 20000 W
h = 45 m
Volume flow per second = 0.03 m^3 /s
mass flow per second = volume flow per second x density of water
= 0.03 x 1000 = 30 kg/s
Output power = m g h / t = 30 x 10 x 45 = 13500 W
Power converted in form of heat = Input power - Output power
= 20000 - 13500 = 6500 W = 6.5 kW
Thus, mechanical power converted into heat is 6.5 kW.
Answer:
428.59 N
Explanation:
Buoyant force, 
where V is volume, g is gravitational constant and \rho is density
where 
is upward force
where 
is the density of hippo
Using g as 9.81
Therefore, the upward force=428.59 N
Answer:
Diameter decreases by the diameter of 0.0312 m.
Explanation:
Given that,
Bulk modulus = 14.0 × 10¹⁰ N/m²
Diameter d = 2.20 m
Depth = 2.40 km
Pressure = ρ g h = 1030 × 9.81 × 2.4 × 1000
= 24.25 × 10⁶ N/m²
Volume = 
Bulk modulus is equal to
now
Δ r = -0.0156 m
change in diameter
Δ d = -2 × 0.0156
Δ d = -0.0312 m
Diameter decreases by the diameter of 0.0312 m.
They would be likely to be underweight. This is because the role of villi is to increase absorption of soluble molecules, they do this by increasing surface area for absorption to occur across.
If the person has less villi than normal in their small intestine, then the surface area will not be as large meaning there is less area for absorption to occur across so less soluble molecules will be absorbed.
