a. Height of balloon when the rock was thrown
Vertical motion of the stone relative to the ground:
y_stone(t) = h v_b t (1/2) g t²
Substitute values:
0 = h (20)(6) 0.5(9.8)(6²)
0 = h 120 176.4
h = 296.4 = 296 m
Answer: Height of balloon when rock is thrown: 296 m
b. Height of balloon when rock hits the ground
y_balloon = h v_b t = 296.4 20(6) = 176.4 = 176 m
Answer: Height of balloon when stone hits ground: 176 m
c. Horizontal distance of stone from basket
x = v_s t = 15 × 6 = 90 m
Answer: Distance of stone from basket: 90 m
d. Horizontal and vertical velocity components just before hitting the ground
i. Relative to basket
Horizontal: v_x = 15 m/s
Vertical: v_y = g t = 9.8 × 6 = 58.8 59 m/s
Answer (relative to basket): v_x = 15 m/s, v_y = 59 m/s
ii. Relative to ground
Horizontal: v_x = 15 m/s
Vertical: v_y = v_balloon + v_stone relative to balloon = 20 + ( 58.8) = 38.8 = 39 m/s
Answer (relative to ground): v_x = 15 m/s, v_y = 39 m/s
Summary:
a) 296 m
b) 176 m
c) 90 m
d) Relative to basket: v_x = 15 m/s, v_y = 59 m/s; Relative to ground: v_x = 15 m/s, v_y = 39 m/s