1. **Problem 1: Find the vertical component of the velocity of a football kicked at 40 ft/s at a 30° angle with the ground.** 2. The formula for the vertical component of velocity is: $$v_y = v \sin(\theta)$$ where $v$ is the initial speed and $\theta$ is the angle with the horizontal. 3. Substitute the given values: $$v_y = 40 \times \sin(30^\circ)$$ 4. Recall that $\sin(30^\circ) = \frac{1}{2}$, so: $$v_y = 40 \times \frac{1}{2} = 20$$ 5. Therefore, the vertical component of the velocity is $20$ ft/s. --- 1. **Problem 2: Find the horizontal component of the velocity of a ship moving at 100 km/h at a 60° angle with the horizontal.** 2. The formula for the horizontal component of velocity is: $$v_x = v \cos(\theta)$$ 3. Substitute the given values: $$v_x = 100 \times \cos(60^\circ)$$ 4. Recall that $\cos(60^\circ) = \frac{1}{2}$, so: $$v_x = 100 \times \frac{1}{2} = 50$$ 5. Therefore, the horizontal component of the velocity is $50$ km/h. --- 1. **Problem 3: Determine the relationship between vectors $a$ and $b$ shown in the figure.** 2. Since vectors $a$ and $b$ point in roughly the same direction but are not collinear, they are **parallel** but not equal. 3. Therefore, the correct answer is: متوازيان (parallel). --- 1. **Problem 4: Identify the vector representing the resultant of vectors $u$ and $v$ in the triangle formed by $u$, $v$, and $w$.** 2. In a closed triangle formed by vectors $u$, $v$, and $w$, the resultant of $u$ and $v$ is the vector $-w$ (the vector that closes the triangle). 3. Therefore, the vector representing the resultant of $u$ and $v$ is $w$ (with opposite direction). 4. The correct answer is: $w$.