Question

An airplane is in level flight at a velocity of \[500km/h\] and an altitude of \[1500m\] when a wheel falls off.
(a)How long does the wheel take to reach the ground?
(b)What horizontal distance will the wheel travel before it strikes the ground?
(c)What will the wheel’s velocity be when it strikes the ground?

Answer 1

Hint: Although an object moving upwards is not normally regarded to be falling, if it is simply subjected to gravity, it is said to be in free fall.
The force of gravity causes objects to descend toward the Earth's center. As a result, gravity-induced acceleration is employed to characterize the acceleration of free-falling objects.
An object in free fall in a vacuum at the Earth's surface accelerates at approximately\[9.8{\text{ }}m/{s^2}\] , regardless of its mass.

Complete step-by-step solution:
Given,
\[h = 1500m\]
When an object is dropped (rather than hurled) from a great height, its initial velocity is 0 m/s.
So Initially vertical velocity, \[u = 0\]
So in the vertical direction,
\[u = 0\], \[h = 1500m\]
\[h = ut + \dfrac{1}{2}a{t^2}\]
\[1500 = 0 \times (t) + \dfrac{1}{2} \times 10 \times {t^2}\]
\[{t^2} = \dfrac{{3000}}{{10}} = 300\]
\[t = \sqrt {300} = 17.55\sec \]
(a)Answer: \[t = 17.55\sec \]
 There is no force in the horizontal direction
So in horizontal
Distance = velocity\[ \times \]time
Given,
Velocity\[ = 500km/h = 500 \times \dfrac{5}{{18}}m/\operatorname{s} \]
Now,
Distance \[ = \;(500) \times \dfrac{5}{{18}} \times 17.55 = 2433m = 2.43km\]
(b)Answer: \[2.43km\]
Now,
Vertical velocity,\[v = u + at\]
\[v = 0 + 10 \times 17.5 = 175m/s\]
net velocity,
\[{v_1} = 500 \times \dfrac{5}{{18}} = 139m/sec\]
\[\therefore \sqrt {{{175}^2} + {{139}^2}} = \sqrt {30625 + 19321} = \sqrt {49946} = 222m/\sec \]

Note: When an object falls through a vacuum, it is solely subjected to one external force: gravity, which is quantified as the object's weight. A free-falling item moves solely due to gravity's action, and its motion is described by Newton's second law of motion.
When an object is dropped and encounters air resistance, the object will eventually achieve a terminal velocity.
Air resistance opposes an object's motion through the air, whereas friction opposes motion between items and the medium they are passing through.