Answer:
The rotational angular speed is measured at 1.34 rad/s.
Explanation:
Considering the following parameters,
Length = 3.40 m
Distance = 5.90 m
Angle = 45.0°
We are tasked with finding the angular speed of rotation
Using the balance equation
Horizontal component
Vertical component
Substituting the tension value
Substituting the value into the equation
Thus, the angular speed of rotation computes to 1.34 rad/s.
Answer:
θ = 61.3°
Alicia must swim at an angle of 61.3°
Explanation:
Parameters given include:
Width of the river = 100 m
Alicia's speed in still water = 2.5 m/s
Speed of river's current = 1.2 m/s
The angle she needs to swim can be determined by combining the velocities, taking into account the current's influence.
Her swimming speed aimed against the current must offset the current's velocity;
2.5cosθ - 1.2 = 0
2.5cosθ = 1.2
cosθ = 1.2/2.5
θ = cosinverse(1.2/2.5)
θ = 61.3°
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.
