Answer:
8.85437 m/s
Explanation:
m = Mass of sphere = 5 kg
h = Vertical height = 4 m
g = Acceleration due to gravity = 9.80 m/s²
Applying conservation of energy we get




The sphere's speed when it reaches the bottom of the ramp is 8.85437 m/s
In component form, the displacement vectors become
• 350 m [S] ==> (0, -350) m
• 400 m [E 20° N] ==> (400 cos(20°), 400 sin(20°)) m
(which I interpret to mean 20° north of east]
• 550 m [N 10° W] ==> (550 cos(100°), 550 sin(100°)) m
Then the student's total displacement is the sum of these:
(0 + 400 cos(20°) + 550 cos(100°), -350 + 400 sin(20°) + 550 sin(100°)) m
≈ (280.371, 328.452) m
which leaves the student a distance of about 431.8 m from their starting point in a direction of around arctan(328.452/280.371) ≈ 50° from the horizontal, i.e. approximately 431.8 m [E 50° N].
Answer:
41.4 g
41.4 cm³
1.08695 g/cm³
Explanation:
= Density of water = 1 g/cm³
Mass of water displaced will be the difference of the

Mass of water displaced is 41.4 g
Density is given by

So, volume of bone is 41.4 cm³
Average density of the bird is given by

The average density is 1.08695 g/cm³