100A #85012 QUIZ 2

1. A projectile is thrown upward with an initial speed of 40m/s and 30° above the horizontal. (a) Find its velocity in 3.0s. (b) Approximately locate the position of the projectile at t = 3.0s in the diagram, and sketch the velocity vector as the sum of their components.

Solution.

(a) We find the components of the initial velocity from

                  v_x = v_0x= v₀cosq₀ = (40m/s)cos30° = 34.64m/s.

                  v_0x = v₀sinq₀ = (40m/s)sin30° = 20m/s.

     We find the vertical component of the velocity in 5s from

                  v_y= v_0y - gt = (20m/s) - (9.80m/s²)(3.0s) = -9.40m/s.

    We find the magnitude of the velocity from

                  v = (v_x² + v_y²)^1/2 = [(34.64m/s)² + (9.40m/s)²)]^1/2 = 35.7m/s.

    We find the direction of the velocity from

                 tanq = v_y/v_x = (-9.4m/s)/(34.64m/s) = -0.2714, which gives q  = 15.2°.(below +x)

(b) Approximately locate the position of the projectile at t = 3.0s in the diagram, and sketch the velocity vector as the sum of their components.