Answer:
=3.5 m/s
Explanation:
y = x tanθ - 1/2 g x² / (u²cos²θ )
y = 0.25 , x = 0.5, θ = 40°
.25 = .50 tan40 - .5 x 9.8x x²/ u²cos²40
.25 = .42 - 2.0875/u²
u = 3.5 m / s.
Since the Earth is almost spherical in shape, we are actually to find first the volume of the spherical segment at a depth of 1,000 m. The radius of the Earth is 6,371,000 meters. The volume of a spherical segment is:
V = 1/3*πh²(3r - h)
Substituting the values and making sure the units is in mm,
V = 1/3*π(1000 m * 1000 mm/1 m)²[3(6,371,000 m * 1000 mm/1 m) - (1000 m * 1000 mm/1 m)]
V = 2×10²² mm³
Thus, the total amount of bacteria is:
2×10²² mm³ * 100 bacteria/1 mm³ = 2×10²⁴ bacteria
Answer: (a) The magnitude of its temperature change in degrees Celsius is
.
(b) The magnitude of the temperature change (change in T = 15.1 K) in degrees Fahrenheit is
.
Explanation:
(a) Expression for change in temperature is as follows.

= 15.1 K
= 
= 
= 
Therefore, the magnitude of its temperature change in degrees Celsius is
.
(b) Change in temperature from Celsius to Fahrenheit is as follows.
F = 1.8C + 32
C = 
Since, K = C + 273
or, 

= 1.8 (15.1)
= 
or, = 
Thus, we can conclude that the magnitude of the temperature change (change in T = 15.1 K) in degrees Fahrenheit is
.