All objects in orbit must follow the path of an ellipse (one of Keplers laws)
Hi there!
We can begin by finding the acceleration of the block.
Use the kinematic equation:

The block starts from rest, so:

Now, we can do a summation of forces of the block using Newton's Second Law:

mb = mass of the block
T = tension of string
Solve for tension:

Now, we can do a summation of torques for the wheel:

Rewrite:

We solved that the linear acceleration is 1.5 m/s², so we can solve for the angular acceleration using the following:

Now, plug in the values into the equation:

Answer:
The velocity of each ball after the collision are 2.19 m/s and 2.58 m/s.
Explanation:
Given that,
Mass of object = 5 kg
Speed = 3 m/s
Mass of stationary object = 3 kg
Moving object deflected = 30°
Stationary object deflected = 31°
We need to calculate the velocity of each ball after collision
Using conservation of momentum
Along x-axis

Put the value into the fomrula


....(I)
Along y -axis

Put the value into the formula

...(II)
From equation (I) and (II)


Put the value of v₁ in equation (I)



Hence, The velocity of each ball after the collision are 2.19 m/s and 2.58 m/s.
I can't eliminate answers. Some of them are just wrong. A is incorrect. There is no such thing as a 1 pole magnet.
I wouldn't use B. If it is just a bar it is not a magnet.
C is the traditional answer
D is a space filler. It is just there to occupy a letter.
Answer:
a) 69.3 m/s
b) 18.84 s
Explanation:
Let the initial velocity = u
The vertical and horizontal components of the velocity is given by uᵧ and uₓ respectively
uᵧ = u sin 40° = 0.6428 u
uₓ = u cos 40° = 0.766 u
We're given that the horizontal distance travelled by the projectile rock (Range) = 1 km = 1000 m
The range of a projectile motion is given as
R = uₓt
where t = total time of flight
1000 = 0.766 ut
ut = 1305.5
The vertical distance travelled by the projectile rocks,
y = uᵧ t - (1/2)gt²
y = - 900 m (900 m below the crater's level)
-900 = 0.6428 ut - 4.9t²
Recall, ut = 1305.5
-900 = 0.6428(1305.5) - 4.9 t²
4.9t² = 839.1754 + 900
4.9t² = 1739.1754
t = 18.84 s
Recall again, ut = 1305.5
u = 1305.5/18.84 = 69.3 m/s