Answer: 4.8 s
Explanation:
We have the following data:
the mass of the raft
the force applied by Sawyer
the raft's final speed
the raft's initial speed (assuming it starts from rest)
We have to find the time 
Well, according to Newton's second law of motion we have:
(1)
Where
is the acceleration, which can be expressed as:
(2)
Substituting (2) in (1):
(3)
Where 
Isolating
from (3):
(4)
Finally:
Answer:
θ₀ = 84.78° (OR) 5.22°
Explanation:
This situation can be treated as projectile motion. The parameters of this projectile motion are:
R = Range of Projectile = 150 m
V₀ = Launch Speed of Projectile = 90 m/s
g = 9.8 m/s²
θ₀ = Launch angle (OR) Angle of Elevation = ?
The formula for range of a projectile is given as:
R = V₀² Sin 2θ₀/g
Sin 2θ₀ = Rg/V₀²
Sin 2θ₀ = (150 m)(9.8 m/s²)/(90 m/s)²
2θ₀ = Sin⁻¹ (0.18)
θ₀ = 10.45°/2
<u>θ₀ = 5.22°</u>
Also, we know that for the same launch velocity the range will be same for complementary angles. Therefore, another possible value of angle is:
θ₀ = 90° - 5.22°
<u>θ₀ = 84.78°</u>
Answer:
A volume of a cubic meter of water from the surface of the lake has been compressed in 0.004 cubic meters.
Explanation:
The bulk modulus is represented by the following differential equation:

Where:
- Bulk module, measured in pascals.
- Sample volume, measured in cubic meters.
- Local pressure, measured in pascals.
Now, let suppose that bulk remains constant, so that differential equation can be reduced into a first-order linear non-homogeneous differential equation with separable variables:

This resultant expression is solved by definite integration and algebraic handling:




The final volume is predicted by:

If
,
and
, then:


Change in volume due to increasure on pressure is:



A volume of a cubic meter of water from the surface of the lake has been compressed in 0.004 cubic meters.