Part 2. Problems: 50% (2 problems 25% each)
Solve with details each of the below two problems
Problem 1: A batter hits a baseball so that it leaves the bat at speed $v_0 = 50$ m/s at
an angle $\alpha_0 = \frac{\pi}{4}$.
(a) Find the coordinates $[x(t), y(t)]$ as functions of time $t$. (6 pts)
(b) Find the position of the ball and its velocity (magnitude and direction) at $t = 1.2$ s.
(4 pts)
School of Physics and Electronic Information Engineering
Undergraduate student majoring in Engineering
(c) Find the time when the ball reaches the highest point of its flight and deduce the
position of the ball and its velocity (magnitude and direction) at that time. (8 pts)
(d) Find the horizontal range $R$, that is, the horizontal distance from the starting point to
where the ball hits the ground. (7 pts)
Problem 2: Two particles of mass of 2400 kg each are moving along the same track.
One particle is moving with the velocity $v_1$ East, while the other travels with the velocity
of $v_2$ West. The two particles collide and stick together as one mass.
(a) Find, step by step, the expression of the final velocity $v_{1f}$ and $v_{2f}$ of each of the two
objects after the collision (12 pts).
(b) Taking $v_1 = 50$ m/s and $v_2 = 45$ m/s, find the numerical value of $v_{1f}$ and $v_{2f}$ (6.5
pts).
(c) Find the direction (East or West) of motion of each object after the collision, if $v_1 = 50$
m/s and $v_2 = 45$ m/s, (6.5 pts).
