Question

1. coach blake kicks a sportsball up at a 15 degree angle, with a total velocity of 8 m/s.

a. draw a diagram of the initial situation, labeling the total velocity, the initial horizontal and vertical components, and the angle.

Explanation:

Step1: Calculate horizontal component

The formula for horizontal component \(v_x\) of velocity \(v\) at angle \(\theta\) is \(v_x = v\cos\theta\).
Given \(v = 8\ m/s\) and \(\theta=15^{\circ}\), so \(v_x = 8\cos15^{\circ}\approx8\times0.966 = 7.73\ m/s\).

Step2: Calculate vertical component

The formula for vertical component \(v_y\) of velocity \(v\) at angle \(\theta\) is \(v_y = v\sin\theta\).
Given \(v = 8\ m/s\) and \(\theta = 15^{\circ}\), so \(v_y=8\sin15^{\circ}\approx8\times0.259 = 2.07\ m/s\).

Answer:

For the diagram: Draw a vector representing the total velocity \(v = 8\ m/s\) at an angle \(\theta = 15^{\circ}\) with the horizontal. From the end - point of this vector, draw a vertical line (representing \(v_y\approx2.07\ m/s\)) and a horizontal line (representing \(v_x\approx7.73\ m/s\)) to form a right - triangle with the total velocity vector as the hypotenuse. Label the total velocity \(v = 8\ m/s\), the horizontal component \(v_x\approx7.73\ m/s\), the vertical component \(v_y\approx2.07\ m/s\) and the angle \(\theta = 15^{\circ}\).