4. A plane traveling at 200 m/s drops supplies from 1500 m above the ground. If it reaches
1 answer:
Answer:
3500 m
Explanation:
To find the horizontal displacement of the box of supplies, we just need to analyze its horizontal motion.
The horizontal motion of the box is a uniform motion with constant velocity, since there are no forces acting along this direction. Therefore, the horizontal displacement is given by
where
is the horizontal velocity
t is the time
The horizontal velocity of the supplies is the same as the plane, therefore
So, since the time of flight is
t = 17.5 s
The horizontal displacement is
You might be interested in
Answer:
(a) L = 0·73 m
(b) 4·39 × J
Explanation:
(a) From the figure, consider the torque about the point where the rod is attached because if we consider another point then there will be hinge forces acting on the rod at the point of attachment
Let L m be the length of the rod and β be the angle between the rod and the vertical
Let α be the angular acceleration of the rod
As the force of gravity acts at the centre so from the figure, the torque about the point of attachment will be 0·53 × g ×(L ÷ 2) ×sinβ
Assuming that the value of amplitude of this oscillation to be small
As torque = moment of inertia × angular acceleration
0·53 × g ×(L ÷ 2) ×sinβ = ((0·53 × L²) ÷ 3) × α (∵ moment of inertia of the rod from the point of attachment)
<h3>For small oscillations, α = ω² × β</h3>After substituting the value of α and solving we get
ω = √((3 × g) ÷ (2 × L))
Time period = (2 × π) ÷ ω = (2 × π) ÷ √((3 × g) ÷ (2 × L))
∴ (2 × π) ÷ √((3 × g) ÷ (2 × L)) = 1·4
Substituting the value of g as 9·8 m/s² and solving we get
L = 0·73 m
(b) At the maximum amplitude condition the velocity will be 0 and potential energy will be maximum and maximum kinetic energy will be attained at the lowest point and hinge forces will not do work as the point of attachment is not moving
∴ Taking the reference for finding the potential energy as the lowest point
<h3>Maximum potential energy = Maximum kinetic energy </h3><h3>As total energy is constant, since there is no dissipative force</h3>Maximum potential energy = (0·53 × g × L ×(1 - cosβ)) ÷ 2 (∵ increment in height is (L × (1 - cosβ)) ÷ 2
∴ Maximum potential energy = (0·53 × g × L ×(1 - cosβ)) ÷ 2 After substituting the value we get
Maximum potential energy = 4·39 × J
∴ Maximum kinetic energy = 4·39 × J
