Answer:
Find the vector parallel to the resultant of the vector A=i +4j-2k and B=3i-5j+k
2 answers:
Answer:
Explanation:
<u>Vectors in 3D</u>
Given a vector
A vector parallel to
is:
Where k is any constant different from zero.
We are given the vectors:
It's not specified what the 'resultant' is about, we'll assume it's the result of the sum of both vectors, thus:
Adding each component separately:
To find a vector parallel to the sum, we select k=2:
Thus one vector parallel to the resultant of both vectors is:
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Answer:
The coupled velocity of both the blocks is 1.92 m/s.
Explanation:
Given that,
Mass of block A,
Initial speed of block A,
Mass of block B,
Initial speed of block B,
It is mentioned that if the two blocks couple together after collision. We need to find the common velocity immediately after collision. We know that due to coupling, it becomes the case of inelastic collision. Using the conservation of linear momentum. Let V is the coupled velocity of both the blocks. So,
So, the coupled velocity of both the blocks is 1.92 m/s. Hence, this is the required solution.
1) See graph in attachment
2) 10 s
3) 50 m
Explanation:
1)
In this problem, we have an object initially moving with a velocity of
v = 10 m/s
when the time is
t = 0 s
Then, we are told that the speed of the object is decreasing by 1 m/s every second. This means that on a velocity-time graph, the motion will be represented by a straight line, starting from v = 10 when t = 0, and decreasing by 1 m/s every second.
The result can be found in the graph in attachment.
Moreover, we can also infer that the motion of the object is accelerated (because velocity is changing), and that the acceleration is constant and it is equal to
which is equivalent to the gradient of the line in the velocity-time graph.
2)
In this part, we want to find after what time the body will stop its motion.
To do that, we can use the following suvat equation:
where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
In this problem:
u = 10 m/s is the initial velocity of the body
is the acceleration
v = 0 m/s, because we want to find the time T at which the body will stop
Re-arranging the equation, we find:
3)
In order to find the total distance covered by the body during its accelerated motion, we have to use another suvat equation:
where
s is the distance covered
u is the initial velocity
t is the time
a is the acceleration
In this problem:
u = 10 m/s is the initial velocity
is the acceleration
t = 10 s is the time it takes for the body to stop (found in part 2)
Solving for s, we find the distance covered:
