Question

How would you self check this problem?

Squids have been reported to jump from the ocean and travel 30.0m (measured horizontally) before re-entering the water. (a) Calculate the initial speed of the squid if it leaves the water at an angle of 20.0º, assuming negligible lift from the air and negligible air resistance. (b) The squid propels itself by squirting water. What fraction of its mass would it have to eject in order to achieve the speed found in the previous part? The water is ejected at 12.0m/s; gravitational force and friction are neglected. (c) What is unreasonable about the results? (d) Which premise is unreasonable, or which premises are inconsistent?

I know the answers for the problem, I just need to explain how you would self check the problem to make sure you got the correct answers.

Answer 1

Since you already know the answers so self check is given in the end. for self-check there is simple rule use your answer as known value and make one of the given value unknown and try to find that value. if it comes same as given value then that means you got correct answer.

Part A.

Range in projectile motion is given by:

R = (V0^2*sin 2A)/g

V0 = sqrt (R*g/sin 2A) = sqrt (30.0*9.81/sin 40 deg)

V0 = 21.4 m/sec

Part B.

Using rocket propelling equation:

v = ve*ln (m0/m)

m/m0 = exp(-v/ve)

given that, ve = ejection speed of water = 12.0 m/sec

v = initial speed of squid = 21.4 m/sec

m/m0 = exp(-21.4/12.0)

m/m0 = 0.168

fraction of ejected mass will be given by:

N = (m0 - m)/m0 = 1 - (m/m0) = 1 - 0.168 = 0.832

Part C.

Since N = 0.832 = 83.2%, So it's not possible for squid to eject 83% of mass during each jump

Part D.

Since squids are very small creatures, So it's impossible for them to jump 30.0 m in horizontal direction (this is a very long distance, for human world record for long jump is 8.95 m even leopards can jump max 15-20 m)

SELF-CHECK: Suppose initial velocity is 21.4 m/sec at 20 deg launching angle, then

R = (21.4^2*sin 40 deg)/9.81 = 30.00 m

Part B. v = ve*ln (m0/m)

Since we got (m0 - m)/m0 = 0.832 , which gives m/m0 = 0.168, and we got v = 21.4 m/sec in part A, So

ve = v/ln (m0/m) = 21.4/ln(1/0.168) = 12.0 m/sec, So our calculated values are correct.