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
==>
A baseball would hit the bat harder. This is because the baseball is a lot heavier and more dense than the plastic ball. The keyword that you're looking for is density. The baseball is dense.
Explanation:
The law of conservation of mass states that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. According to the law of conservation of mass, the mass of the products in a chemical reaction must equal the mass of the reactants.
5.7 km/h north and 5.8 km/h west are instantaneous velocities, while 8.1 km/h northwest is the average velocity.<span>
The answer choice above is correct.
The instantaneous velocities are the actual </span>velocities while traveling ( the velocity during that instant ). The average velocity is the average of the instantaneous velocities ( the speed in one direction equivalent to the two speeds <span>in different directions ).
I used speed in the explanation because velocity is speed with direction.</span>
As per momentum conservation theory
If net force on a system is zero then initial momentum of the system will be equal to final momentum of that system.
Since initially coconut is at rest so initial momentum is zero
Here it break into three pieces such that two parts of same mass while third part is of double mass
now we can say
here we know that two parts fly off with same speed v0 along south and west directions
now we will have
so here magnitude of the speed of the third part will be
and the direction of the third part will be along North East direction
