HW#26 Ch 9: Center of Mass and Linear Momentum
Instructions: Be sure to write formulas and show substitutions to earn full credit.
1. A baseball bat of length L has a peculiar linear density (mass per unit length) given by \(\lambda = \lambda_0\left(1+\dfrac{x^2}{L^2}\right)\). Find the coordinate of the center of mass in terms of L.
2. A firecracker of mass m and speed v is moving horizontally with respect to Earth when it explodes into three identical fragments. If one fragment of the firecracker moves vertically downward with speed v and a second fragment moves with speed 2v at an angle of 45° above the horizontal, find the velocity \(\vec{v_3}\) of the third fragment in unit vector notation.
3. In a circus act, Adrian (assume mass = 60.0 kg) is shot from a cannon with an initial velocity of 25.0 m/s at an angle of 30° above the horizontal. His partner, Yan, (assume mass = 50.0 kg), stands on an elevated platform located at the top of her trajectory. He grabs her as he flies by and the two fly off together. They land in a net at the same elevation as the cannon a horizontal distance x away. Find x.
4. A soccer ball of mass 0.43 kg leaves the foot of the kicker with an initial speed of 25 m/s. (a) What is the impulse imparted to the ball by the kicker? (b) If the foot of the kicker is in contact with the ball for 0.008 s, what is the average force exerted by the foot on the ball?