Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
At the highest point in its trajectory, the ball's acceleration is zero but its velocity is not zero.
<h3>What's the velocity of the ball at the highest point of the trajectory?</h3>
- At the highest point, the ball doesn't go more high. So its vertical velocity is zero.
- However, the ball moves horizontal, so its horizontal component of velocity is non - zero i.e. u×cosθ.
- u= initial velocity, θ= angle of projection
<h3>What's the acceleration of the ball at the highest point of projectile?</h3>
- During the whole projectile motion, the earth exerts the gravitational force with a acceleration of gravity along vertical direction.
- But as there's no acceleration along vertical direction, so the acceleration along vertical direction is zero.
Thus, we can conclude that the acceleration is zero and velocity is non-zero at the highest point projectile motion.
Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Player kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory
A- neither the ball's velocity nor its acceleration are zero.
B- the ball's acceleration points upward.
C- the ball's acceleration is zero but its velocity is not zero.
D- the ball's velocity points downward.
Learn more about the projectile motion here:
brainly.com/question/24216590
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Water vapor and carbon dioxide
Answer:
5694000 min
Explanation:
Let's suppose the average American watches 4 hours of TV every day. First, we will calculate how many minutes they watch per day. We will use the conversion factor 1 h = 60 min.
(4 h/day) × (60 min/1 h) = 240 min/day
They watch 240 minutes of TV per day. Now, let's calculate how many minutes they watch per year. We will use the conversion factor 1 year = 365 day.
240 min/day × (365 day/year) = 87600 min/year
They watch 87600 min/year. Finally, let's calculate how many minutes they spend watching TV in 65 years.
87600 min/year × 65 year = 5694000 min
Answer: C (impulse acting on the object)
The momentum is defined as it is the impulse acting on the force . Change in momentum is known as Impulse. Impulse is used to increase or decrease the momentum of object.
From Newtons II law
F = m. a
= m. v/t <em>since a = rate of change of velocity.</em>
<em> </em>F . t = m . v
F . t is known as impulse momentum
