Cyclist A and B cycled atan average speed of 15 km/h and 20 km/h respectively from the same starting point X on the same route. Cyclist B started his journey 6 mins after cyclist A had started. i) What were the distances travelled by cyclist A and B 1 h cyclist A had started his journey from point X? ii) Dis cyclist B overtake cyclist A within the first hour of cyclist A's journey?

i. Cyclist A travelled 15 km 1 h cyclist A had started his journey from point X

  Cyclist B travelled 18 km 1 h cyclist A had started his journey from point X

ii. cyclist B overtake cyclist A 6 km from the same starting point X.

Explanation:

From the question,

- Cyclist A and B cycled at an average speed of 15 km/h and 20 km/h respectively.

- Cyclist B started his journey 6 mins after cyclist A had started.

Let the cyclist A time be t.

Then, we can write that

For Cyclist A

Speed = 15 km/h

Time = t mins

For Cyclist B

Speed = 20 km/h

Time = (t - 6) mins

i) To determine the distances travelled by cyclist A and B 1h cyclist A had started his journey,

For Cyclist A

Speed = 15km/h

Time = 1h = 60 mins

From the formula

Speed = Distance / Time

Then,

Distance = Speed × Time

Putting the values into the equation,

Distance = 15km/h × 1h

Distance = 15 km

∴ Cyclist A travelled 15 km 1 h cyclist A had started his journey from point X

For cyclist B

Speed = 20km/h

Time = 1h - 6mins = 60mins - 6mins = 54mins = 54/60 hour = 0.9 h

Also, from

Distance = Speed × Time

Putting the values into the equation

Distance = 20km/h × 0.9h

Distance = 18 km

∴ Cyclist B travelled 18 km 1 h cyclist A had started his journey from point X

ii) To determine the distance cyclist B overtake cyclist A, that is, when the distance covered by cyclist A equals that covered by cyclist B.

First, we will determine the time at which the distances covered by both cyclists were equal.

From

For Cyclist A

Speed = 15 km/h

Time = t hour  

Distance = Speed × Time

Distance = 15t km

For Cyclist B

Speed = 20 km/h

Time = (60t - 6) mins = (t - 0.1) hour

Distance = 20 × (t - 0.1) = (20t - 2) km

Equate the distances

15t = 20t - 2

15t - 20t = -2

-5t = -2

5t = 2

t = 2/5

t = 0.4 hour

Hence, cyclist B overtake cyclist A 0.4 hour after cyclist A had started.

For the distance cyclist B overtake cyclist A,

From

Distance = (20t - 2) km

Distance = (20×0.4 - 2) km

Distance = (8 - 2) km

Distance = 6 km

Hence, cyclist B overtake cyclist A 6km from the same starting point X.

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: