Answer:
Speeds of 1.83 m/s and 6.83 m/s
Explanation:
Based on the law of conservation of momentum,
where m represents mass, 
is the initial speed before impact, 
and 
are the velocities of the impacted object after the collision and of the originally stationary object after the impact.
Thus, 
After the collision, the kinetic energy doubles, therefore:
Substituting the initial velocity of 5 m/s provides the equation needed to proceed.
We know that leads to 
Using the quadratic formula leads us to solve for the speeds after the explosion, specifically where a=2, b=-10, and c=-25. 
By substituting the values, the solution yields results for the speeds of the blocks, which are ultimately 1.83 m/s and 6.83 m/s.
Answer: Her velocity magnitude (v) relative to the shore is 5.70 km/h.
Explanation:
Let Q be the speed of the boat, and P be the speed of the river flow.
R represents the resultant velocity combining boat velocity and river current.
According to vector addition using the law of triangles:
From the diagram:
P = 3.5 km/h, Q = 4.5 km/h
Therefore, her velocity magnitude relative to the shore is 5.70 km/h.
The question pertains to the change in frequency of a wave noted by an observer moving in relation to the source, indicating that the concept to invoke is "
Doppler's effect."
The standard formula for the Doppler effect is:
-- (A)
Note that we don’t need to be concerned with the signs here, as all entities are moving toward each other. If something was moving away, a negative sign would apply, but that is not relevant to this scenario.
Where,
g = Speed of sound = 340m/s.
= Velocity of the observer relative to the medium =?.
= Velocity of the source in relation to the medium = 0 m/s.
= Frequency emitted from the source = 400 Hz.
= Frequency recognized by the observer = 408 Hz.
Substituting the given values into equation (A) will yield:
Solving the above will result in,
= 6.8 m/s
The correct result = 6.8m/s
