Questions: SpaceX launched another rocket at a 60-degree angle has an 1 m / s. Draw an annotated diagram and solve the problem in the space provided below.

Solution Steps

• A rocket is launched at a 60-degree angle with an initial speed of \(1 \, \text{m/s}\).
• We need to analyze the motion of the rocket using the given angle and speed.

• The initial velocity can be broken down into horizontal and vertical components.
• Use trigonometric functions to find these components:
  • Horizontal component: \( v_x = v \cdot \cos(\theta) \)
  • Vertical component: \( v_y = v \cdot \sin(\theta) \)
• Given \( v = 1 \, \text{m/s} \) and \( \theta = 60^\circ \):
  • \( v_x = 1 \cdot \cos(60^\circ) = 0.5 \, \text{m/s} \)
  • \( v_y = 1 \cdot \sin(60^\circ) = \frac{\sqrt{3}}{2} \, \text{m/s} \)

• Draw a right triangle to represent the velocity components.
• Label the hypotenuse as \(1 \, \text{m/s}\).
• Label the angle between the hypotenuse and the horizontal as \(60^\circ\).
• Label the horizontal side as \(0.5 \, \text{m/s}\).
• Label the vertical side as \(\frac{\sqrt{3}}{2} \, \text{m/s}\).

• The horizontal motion is uniform with velocity \(v_x = 0.5 \, \text{m/s}\).
• The vertical motion is subject to gravitational acceleration \(g = 9.81 \, \text{m/s}^2\).
• Use kinematic equations to analyze the vertical motion if needed.

Final Answer