What does a 12 kg mass weigh on the Moon?
1 answer:
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Explanation:
It is given that,
Angular frequency,
Maximum displacement, A = 0.5 m at t = 0 s
We need to find the time at which it reaches its maximum speed. Firstly, we will find the maximum velocity of the object that is exhibiting SHM.
............(1)
Acceleration of the object,
...............(2)
Using first equation of motion we can calculate the time taken to reach maximum speed.
t = 0.25 s
So, the object will take 0.25 seconds to reach its maximum speed. Hence, this is the required solution.
First of all, let's write the equation of motions on both horizontal (x) and vertical (y) axis. It's a uniform motion on the x-axis, with constant speed 
, and an accelerated motion on the y-axis, with initial speed 
and acceleration 
:
where the negative sign in front of g means the acceleration points towards negative direction of y-axis (downward).
To find the distance from the landing point, we should find first the time at which the projectile hits the ground. This can be found by requiring
Therefore:
which has two solutions:
is the time of the beginning of the motion,
is the time at which the projectile hits the ground.
Now, we can find the distance covered on the horizontal axis during this time, and this is the distance from launching to landing point:
where the negative sign in front of g means the acceleration points towards negative direction of y-axis (downward).
To find the distance from the landing point, we should find first the time at which the projectile hits the ground. This can be found by requiring
Therefore:
which has two solutions:
Now, we can find the distance covered on the horizontal axis during this time, and this is the distance from launching to landing point: