A father racing his son has half the kinetic energy of the son, who has half the mass of the father. The father speeds up by 1.0 m/s and then has the same kinetic energy as the son. What are the original speeds of (a) the father and (b) the son

a. 2.41 m/s

b. 4.82 m/s

Explanation:

Father's KE is:

K. E. = ½mv²

Sons k. e. is:

k. e. = ½MV²

Since M = ½m:

k. e. = ¼mV²

We are given that K. E. = ½k.e., therefore:

½mv² = ½(¼mV²)

½mv² = ⅛mV²

=> v² = V²/4

=> v = V/2 and V = 2v

When the father's speed is (v + 1) m/s, K. E. = k. e.:

K. E. = ½m(v + 1)²

=> ½m(v + 1)² = ¼mV²

(v + 1)² = ½V²

Since V = 2v

=> (v + 1)² = ½(2v)²

v² + 2v + 1 = ½(4v²)

v² + 2v + 1 = 2v²

=> v² - 2v - 1 = 0

=> v = 2.41m/s or -0.41m/s

Since speed cannot be negative:

v = 2.41m/s

Recall that V = 2v

=> V = 2 * 2.41 = 4.82m/s

Hence, the father's speed is 2.41m/s and the son's speed is 4.82m/s.

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:

6/12=1/2

step-by-step explanation: