Answer
a) See the answer below.
b) $29.3\;\rm m$ to the west.
Work Step by Step
a) Two kids are playing gunfire, the first one was moving toward the east at a constant speed of 3 m/s when he saw his enemy (the other kid) hiding 100 m away to the north from him.
He decided to shoot him with his toy gun, and the shot was released while he is running at a speed of 6 m/s with an angle 45$^\circ$ north of the east. where is the kid after the shot hits his enemy?
b)
From the first given formula;
$$v_x=-1.243\;\rm m/s$$
From the second given formula;
$$v_y=4.243\;\rm m/s$$
From the third given formula;
$$t_1=\dfrac{100}{v_y}=\dfrac{100}{4.243}=23.6\;\rm s$$
Thus, and from the fourth given formula;
$$x_1=23.6\cdot -1.243=-29.3\;\rm m$$
This means that the enemy kid will be 29.3 m-west of our hero kid.
