A bird is flying horizontally over level ground at a steady

Question

Q1. A bird is flying horizontally over level ground at a steady known speed v (m/s). As it flies, bird releases a stone ("drops" it) from its beak. The stone then falls freely as a projectile. The stone makes half of its total altitude change during the final t seconds of its fall. What was the average velocity of the stone over the time interval when it was a projectile?

Q2. Two particles, A and B, move in the x-y coordinate plane, according to these time functions (all lengths are in meters, and all times are in seconds):

 v_A(t) = [4t, 2] m/s            r_A(0) = [-7, 3] m                r_B(t) = [11, t²] m

a. For 0 ≤ t ≤ 2.00 s, find a_B.avg.

b. Find v_AB(2).

c. Do these particles ever collide? If so, when and where? If not, how do you know they don't? (Show all your work, regardless of your conclusions.)

Q3. Two particles, A and B, move along the x-axis. Their motions are graphed here

Evaluate (T/F/N) each of the following statements. As always, you must fully justify your answer with some valid combination of words, drawings, equations, etc.

a. x_A(t₁) > x_B(t₁)

b. a_A.x(t₂) ≈ a_B.x(t₂)

c. v_BA(t₃) is in the -x-direction.

Q4. Refer to the diagram. ∠0° is defined to the right; ∠90° is vertically upward; ∠-90° is vertically downward.

Projectile A is launched at a known velocity v_i.A∠ θ_i.A from point A at the top of a cliff of height, H. (0 < θ_i.A < 90°)

Projectile B is launched (at some unknown velocity and moment) from point B at the cliff's base.

The projectiles collide at a known height h, which is the peak height for projectile B (and note that h < H).

Find the impact velocity, v_BA (both magnitude and angle).