Question

The propeller on a boat motor is initially rotating at 8 revolutions per second. As the boat captain reduces the boat speed, the propeller SLOWS at a steady rate of 0.9 revolutions per second per second. After 17 revolutions, how fast is the propeller spinning in revolutions per second

Answer 1

Answer: $5.77\ rps$

Explanation:

Given

Initial angular velocity is $\omega_i=8\ rps$

rate of reduction $\alpha=0.9 rev/s^2$

after 17 revolution i.e. $\theta =17\ rev$

using $\Rightarrow \omega_f^2-\omega_i^2=2\alpha\theta$

Insert the values

$\Rightarrow \omega_f^2=8^2-2\times (0.9)\times17\\\Rightarrow \omega_f^2=33.4\\\Rightarrow \omega_f=5.77\ rps$