Robots with telescoping arms are sometimes used to perform tasks (e. g., welding or placing screws) where access may be difficult for other robotic types. During a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. Determine the velocity and acceleration of the robot tip A

a)

b)

Explanation:

a) You have the following motion equation:

The velocity, in polar coordinates, is given by:

You calculate the derivatives:

b) the acceleration is:

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min