The air temperature over a lake decreases linearly with height after sunset, since air cools faster than water. The mean molar mass of air is M=28.8×10−3kg/mol.

The questions are:
If the temperature at the surface is 28.00 ∘C and the temperature at a height of 260.0 m is 8.000 ∘C how long does it take sound to rise 260.0 m directly upward? [Hint: Use the equation v=sqrt(γRT/M) and integrate.]

At a height of 260.0 m, how far does sound travel horizontally in this same time interval?

t = 0.878s

Explanation: Dear big brain

since your temperature decreases linearly, you can assume that your velocity should behave linearly too. Here this isn't exactly the case (cfr. formula). But there's another way to prevent endlessly boring calculus. Use the principle of interpolation. (x/v_surface + x/v_top)/2 = t.

This answer won't be exactly the same, but it's a quite good approx. You can use this eqation, hence you don't use large distances.

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:

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

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