The velocity is given by:
V = √(Vx²+Vy²)
V = velocity, Vx = horizontal velocity, Vy = vertical velocity
Given values:
Vx = 6m/s, Vy = 12m/s
Plug in and solve for V:
V = √(6²+12²)
V = 13.42m/s
Now find the direction:
θ = tan⁻¹(Vy/Vx)
θ = angle of velocity off horizontal, Vy = vertical velocity, Vx = horizontal velocity
Given values:
Vx = 6m/s, Vy = 12m/s
Plug in and solve for θ:
θ = tan⁻¹(12/6)
θ = 63.4°
The resultant velocity is 13.42m/s at an angle of 63.4° off the horizontal.
Answer:
The speed of the ball was, v = 3 m/s
Explanation:
Given data,
The time period of the ball, t = 8 s
The distance the ball rolled, d = 24 m
The velocity of an object is defined as the object's displacement to the time taken. The formula for the velocity is,
v = d / t m/s
Substituting the given values in the above equation,
v = 24 / 8
= 3 m/s
Hence, the speed of the ball was, v = 3 m/s
Answer:

Explanation:
The force on the point charge q exerted by the rod can be found by Coulomb's Law.

Unfortunately, Coulomb's Law is valid for points charges only, and the rod is not a point charge.
In this case, we have to choose an infinitesimal portion on the rod, which is basically a point, and calculate the force exerted by this point, then integrate this small force (dF) over the entire rod.
We will choose an infinitesimal portion from a distance 'x' from the origin, and the length of this portion will be denoted as 'dx'. The charge of this small portion will be 'dq'.
Applying Coulomb's Law:

The direction of the force on 'q' is to the right, since both charges are positive, and they repel each other.
Now, we have to write 'dq' in term of the known quantities.

Now, substitute this into 'dF':

Now we can integrate dF over the rod.

By applying Newton's second law of motion;
ma = mg - T
Where,
m = mass; a = downward accelerations (+ve value) or upward acceleration (-ve value); g = gravitational acceleration; T = tension.
For the current case, the velocity is constant therefore,
a = 0
Then,
0 = mg - T
T = mg = 115*9.81 = 1128.15 N
Tension in the cable is 1128.15 N.
Answer:
Loss, 
Explanation:
Given that,
Mass of particle 1, 
Mass of particle 2, 
Speed of particle 1, 
Speed of particle 2, 
To find,
The magnitude of the loss in kinetic energy after the collision.
Solve,
Two particles stick together in case of inelastic collision. Due to this, some of the kinetic energy gets lost.
Applying the conservation of momentum to find the speed of two particles after the collision.



V = 6.71 m/s
Initial kinetic energy before the collision,



Final kinetic energy after the collision,



Lost in kinetic energy,



Therefore, the magnitude of the loss in kinetic energy after the collision is 10.63 Joules.