Answer:
a. Angle= 28.82°
b. Approved. Although he might feel cold, he should be able to cross.
Explanation:
Velocity Vector
Velocity is a measure of how quickly something is moving in a specific direction. It is represented as a vector that has both magnitude and direction. If an object can only move in one direction, then speed can serve as the scalar equivalent of that velocity (only focusing on magnitude).
a.
The explorer aims to swim across a river to reach his campsite, as depicted in the image below. The river's velocity is vr and the explorer's swimming speed in still water is ve. If he were to swim straight towards the campsite, he would end up downstream due to the river's current. Therefore, he must swim at an angle that allows him to overcome the current while still moving towards his goal. This angle relative to the shore is what we need to determine. The explorer's speed can be broken down into its horizontal (vx) and vertical (vy) components. In order to counteract the river's flow:
We can calculate the vertical component of the explorer's swimming speed as
Thus
Finding the value of
Then the angle is given by
b.
The component of the explorer's velocity that goes horizontally is
This represents the actual velocity directed towards the campsite
Considering that
To find t
Calculating the duration for the explorer to cross the river
As this time is under the hypothermia threshold (300 seconds), the conclusion is
Approved. Although he will feel cold, he should manage to cross successfully.
Result: -50.005 kJ
Details:
Provided Data
mass of the system = 10 kg
work done = 0.147 kJ/kg
Elevation change
initial speed
Final Speed
Specific internal Energy
according to the first Law of thermodynamics
where KE represents kinetic energy
PE indicates potential energy
U denotes internal Energy
Q = 1.47 + 3.375 - 4.850 - 50
Q = -50.005 kJ
Answer:
Height (h) = 17 m
Velocity (v) = 18.6 m/s
Explanation: This problem can be solved using kinematic motion equations.
Given Data
Initial velocity (u) = 0
Acceleration (a) = g
Time (t) = 1.9 seconds
First, we calculate the height.
Then, we find the final velocity
The acceleration graph is a linear representation described by y=9.8, as it remains constant:
The velocity graph can be represented by y=9.8x (where y signifies velocity and x indicates time):
The displacement graph can be described as y=4.9x^2 (with x as time and y as displacement):
These graphs apply exclusively from x=0 to x=1.9, so disregard other sections of the graphs.
Answer:
Explanation:
The stone reaches the top of the flagpole at both t = 0.5 s and t = 4.1 s
therefore, the total duration of the upwards motion above the peak of the pole is provided as
now we have
this indicates the speed at the flagpole's top
at this point we have
the height of the flagpole is stated as
Answer:
Explanation:
Refer to the attached diagram for enhanced clarity regarding the question.
One of the blocks weighs 1.0 kg and accelerates downward at 3/4g.
g denotes the acceleration due to gravity.
Let M represent the block with known mass, while 'm' signifies the mass of the other block and 'a' refers to the acceleration of body M.
Given M = 1.0 kg and a = 3/4g.
By applying Newton's second law;
For the body with mass m;
T - mg = ma... (1)
For the body with mass M;
Mg - T = Ma... (2)
Combining equations 1 and 2 gives;
+Mg -mg = ma + Ma
Ma-Mg = -mg-ma
M(a-g) = -m(a+g)
Substituting M = 1.0 kg and a = 3/4g into this equation leads to;
3/4 g-g = -m(3/4 g+g)
3/4 g-g = -m(7/4 g)
-g/4 = -m(7/4 g)
1/4 = 7m/4
Multiplying gives: 28m = 4
m = 1/7 kg
Hence, the mass of the other box is 1/7 kg
