Seafloor spreading causes an oceanic plate to collide with a continental plate. If it were to go through the whole tectonic cycl
2 answers:
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Ok, we need to find a relation for the speed as it relates to the acceleration. This is given by the integral of acceleration:
Where we have the initial velocity is 0m/s and a will be 4.90m/s².
But we see there is an issue now... We know the velocity as a function of time, but we don't know how long the car has been accelerating! We need to calculate this time by now finding the position function as a function of time. This way we can solve for the time, t, that it takes to go 200m accelerating this way and then substitute that time into our velocity equation and get the velocity.
Position is just the integral of velocity:
Where the initial velocity and initial position are both zero.
Now we set this position function equal to 200m and find the time, t, it took to get there
Now let's put t=9.04s into our velocity equation:
Where we have the initial velocity is 0m/s and a will be 4.90m/s².
But we see there is an issue now... We know the velocity as a function of time, but we don't know how long the car has been accelerating! We need to calculate this time by now finding the position function as a function of time. This way we can solve for the time, t, that it takes to go 200m accelerating this way and then substitute that time into our velocity equation and get the velocity.
Position is just the integral of velocity:
Where the initial velocity and initial position are both zero.
Now we set this position function equal to 200m and find the time, t, it took to get there
Now let's put t=9.04s into our velocity equation:
<h2>Answer: (a)t=0.553s, (b)x=110.656m</h2>
Explanation:
This situation is a good example of the projectile motion or parabolic motion, in which the travel of the bullet has two components: x-component and y-component. Being their main equations as follows:
x-component:
(1)
Where:
is the bullet's initial speed
because we are told the bullet is shot horizontally
is the time since the bullet is shot until it hits the ground
y-component:
(2)
Where:
is the initial height of the bullet
is the final height of the bullet (when it finally hits the ground)
is the acceleration due gravity
Now, for the first part of this problem, the time the bullet elapsed traveling, we will use equation (2) with the conditions given above:
(3)
(4)
Finding :
(5)
Then we have the time elapsed before the bullet hits the ground:
(6)
For the second part of this problem, we are asked to find how far does the bullet traveled horizontally. This means we have to use the equation (1) related to the x-component:
(1)
Substituting the knonw values and the value of found in (6):
(7)
(8)
Finally: