# What is the maximum velocity?

1. suppose a spaceship is designed to withstand a micrometeorite impact delivering a TKE of million joules, suppose that the most massive micrometeorite has a mass of 3 g, what is the maximum relative velocity of the micrometeorite to the spaceship so that the ship can withstand the impact?

27. to maintain a speed of v on a horizontal road, a car has to produce enough power to overcome air resistance. the required power goes up with increasing speed according to the equation : P=Power in kW= k * V^3

where V is measured in miles/hour and k is a proportionality constant. Suppose it takes a power of 7.7 kW to overcome air resistance at 30.0 mph, find

(a) the value of K in it's appropriate units

(b) using a spreadsheet prepare a graph of power(kW) versus speed (mph) for speeds from 0 mph to 100 mph ((Just tell me what to graph and I'll do it))

Relevance

1. TKE = 1e6 J = ½mv² = ½ * 0.003kg * v²

v ≈ 26 km/s

27. kW units are J/s = N·m/s = (kg·m/s²)(m/s) = (kg/s)(m/s)² ← LHS units

The RHS is in k * (m/s)³. Cancelling (m/s)² leaves

kg/s = k * m/s

THEREFORE units for k are kg/m.

30 mph = 13.4112 m/s, so

7700 = k * (13.4112)³

k = 3.19 kg/m

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