Neglecting gravity, doubling the exhaust velocity from n single stage rocket ini

Question

Neglecting gravity, doubling the exhaust velocity from n single stage rocket initially at rest changes the final velocity attainable by what factor? Assume all other variables, such as the mass of the rocket and the mass of the fuel, do not change. The final velocity stays the same. The final velocity doubles. The final velocity increases by a factor of 0.693. The final velocity increases by a factor of 0.310. A baseball outfielder throws a baseball of mass 0. 15 kg at a speed of 30 m/s and initial angle of 30degree. What is the kinetic energy of the baseball at the highest point of the trajectory? Ignore air friction. Zero 51 J 92 J 120 J Alex throws a 0.43-kg rubber bull down onto the floor. The ball's speed just before impact is 6.5 m/s, and just after is 5.5 m's. What is the magnitude of the change in the ball's momentum? 0.09 kg'm/s 1.0 kg'm/s 4.3 kg'm/s 5.2 kg'm/s The escape speed from the surface of the Earth is 11.2 km's. Estimate the escape speed for a spacecraft from the surface of the Moon. The Moon has a mass 181 that of Earth and a radius 0.25 that of Earth. 2.5 km/s 4.0 km/s 5.6 km/s 8.7 km/s Yuri, a Russian weightlifter. is able to lift 300 kg a distance 2.00 m in 2.00 s. What is.his power output? 500 kW 2.45 kW 2.94 kW 9.80 kW Two masses m_1 and m_2 with m_1 > m_2, have momenta with equal magnitudes. How do their kinetic energies compare? KE_1 KE_2 More information is needed.

Explanation / Answer

11) (Option B is correct) The final velocity doubles.

12) The ball is released at a starting height of 0, at an angle of 30° up from horizontal.
At the highest point of the trajectory the vertical velocity = 0. The horizontal velocity is constant at 30*cos(30°) = 25.98 m/s
E = (1/2) m v^2 = 0.5 x 0.150 x (25.98^2) = 50.625 J (option B is correct)

13) mass(m)= 0.43
initial velocity(u) = -6.5
final velocity(v) = 5.5

Change in momentum = m(v - u) = 0.43*(5.5 + 6.5) = 5.16 kgm/s (option D is correct)

14) Escape Velocity = SQRT(2GM/r)
Basically you need to take the ratio: Let's define some constants
Ve= Escape velocity earth
Vm =Escape Velocity moon
Me=Mass of earth
Mm=Mass of Moon
Re=Radius of Earth
Rm=Radius of Moon
From the question: Ve=11.2 km/s, Mm=Me/81, Rm=0.25 Re
So Ve/ Vm = [sqrt( G Me / re) / sqrt(G Mm / rm)]
= sqrt( (G Me /re) * (rm/G Mm))
= sqrt( (Me/Mm) * ( rm / re))
= sqrt( (Me / (Me /81)) * (0.25 re / re))
= sqrt( 81 * 0.25)
= 4.5
So Ve / Vm = 4.5 --> 11.2 / Vm =4.5 therefore Vm= 11.2/4.5 = 2.5 km/s
So A is the correct answer

15) Power is the time rate of doing work = work/unit time = newton*meter/sec = watt
Power = 300(9.8)(2)/2 (kgm^2/sec^3 = newton*meter/sec = watts)
= 2940 watts = 2.94 kW (option C is correct)

16) Option A is correct as K = p^2/2m

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