A stone thrown horizontally from a height of 6.07 m hits the ground at a distance of 12.30 m. Calculate the initial speed of the stone. Neglect air resistance.

11.16m/s

The motion has both vertical and horizontal components. Using one of the equations of motion as follows;

h = ut + x a x t²

Where;

h = horizontal or vertical displacement

u = initial velocity in the horizontal/vertical motion

a = acceleration in the horizontal/vertical motion

t = time taken for the motion

Now, let's take the horizontal component first. Using the same equation;

h = ut + ( x a x t²)           -----------------(i)

Where;

h = horizontal displacement = 12.30m

a = 0      [acceleration in the horizontal is zero as velocity is constant in that direction]

Substitute these values into equation (i) as follows;

12.30 = ut  + ( x 0 x t²)

12.30 = ut       -------------------------------(ii)

Now, let's take the vertical component. Using the same equation;

h = ut + ( x a x t²)           -----------------(iii)

Where;

h = vertical displacement = 6.07m

a = acceleration due to gravity = +10m/s²      [acceleration in the vertical is the acceleration due to gravity which can be positive or negative depending on the direction of motion. +ve if motion is upwards, and -ve if motion is downwards. In our case, the motion is downwards, hence +ve gravity]

u = 0        [there is no velocity in the vertical motion since the stone is thrown horizontally]

Substitute these values into equation (iii) as follows;

=> 6.07 = ut + ( x 10 x t²)    

=> 6.07 = ut + 5t²     ---------------------(iv)

Substitute this into equation (iv) as follows;

=> 6.07 = 5t²

Solve for t;

=> 5t² = 6.07

=> t² = 6.07 / 5

=> t² = 1.214

=> t =

=> t = 1.102s

Substitute this value of t = 1.102 into equation (ii) as follows;

12.30 = u(1.102)

Solve for u;

u = 12.30 / 1.102

u = 11.16m/s

Therefore, the initial speed of the stone is 11.16m/s

a.

explanation:

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: