Answer:
H = 70.4 m
Explanation:
Here first of all the balloon will drop to the the floor under free fall motion and then the sound of splash will come up at constant speed
so we will say that if the total height is H
so the time to fall is given as
now we have
also we know that the time to come the sound upwards is
so we will have
now plug in all data
by solving above equation we have
H = 70.4 m
Answer:
The two forces are;
1) Force 1 with magnitude of approximately 183.013 N, acting 30° to the left of the resultant force
2) Force 2 with magnitude of approximately 129.41 N acting at an inclination of 45° to the right of the resultant force
Explanation:
The given parameters are;
The (magnitude) of the resultant of two forces = 250 N
The angle of inclination of the two forces to the resultant = 30° and 45°
Let, F₁ and F₂ represent the two forces, we have;
F₁ is inclined 30° to the left of the resultant force and F₂ is inclined 45° to the right of the resultant force
The components of F₁ are = -F₁ × sin(30°)·i + F₁ × cos(30°)·j
The components of F₂ are = F₂ × sin(45°)·i + F₂ × cos(45°)·j
The sum of the forces = F₂ × sin(45°)·i + F₂ × cos(45°)·j + (-F₁ × sin(30°)·i + F₁ × cos(30°)·j) = 250·j
The resultant force, R = 250·j, which is in the y-direction, therefore, the component of the two forces in the x-direction cancel out
We have;
F₂ × sin(45°)·i = F₁ × sin(30°)·i
F₂ ·√2/2 = F₁/2
∴ F₁ = F₂ ·√2
∴ F₂ × cos(45°)·j + F₁ × cos(30°)·j = 250·j
Which gives;
F₂ × cos(45°)·j + F₂ ·√2 × cos(30°)·j = 250·j
F₂ × ((cos(45°) + √2 × cos(30°))·j = 250·j
F₂ × ((√2)/2 × (1 + √3))·j = 250·j
F₂ × ((√2)/2 × (1 + √3))·j = 250·j
F₂ = 250·j/(((√2)/2 × (1 + √3))·j) ≈ 129.41 N
F₂ ≈ 129.41 N
F₁ = √2 × F₂ = √2 × 129.41 N ≈ 183.013 N
F₁ ≈ 183.013 N
The two forces are;
A force with magnitude of approximately 183.013 N is inclined 30° to the left of the resultant force and a force with magnitude of approximately 129.41 N is inclined 45° to the right of the resultant force.
