Question

An airplane is flying horizontally with a velocity of $216\,km/hr$ and at a height of $490\,m$. The total horizontal distance traveled by the packet is ?

Answer 1

In these types of questions you should have prior knowledge about the distance and displacement and also remember that the velocity of the bomb will be the same as the velocity of the airplane, use this information to approach the solution.

Formula used:
$t = \sqrt {\dfrac{{2H}}{g}}$
$\text{distance = speed} \times \text{time}$

Complete step by step answer:
According to the given information velocity of the airplane is $216\,km/hr$ which is at a height of $490\,m$ above from ground, since we know that when a bomb is released from the plane it will have the same velocity as the velocity of the airplane since due to the bomb is thrown from height at speed of $216km/hr$ it will experience a gravitational force due to which the bomb will be in a projectile motion and AB will be the horizontal distance traveled by the bomb.

So the velocity of the bomb is equal to $= 216km/hr = 216 \times \dfrac{5}{{18}} = 60m/s$
Now we know that the bomb is in free fall therefore it will take some time to reach the ground. Let $t$ be the time taken by the bomb to reach the ground
$t = \sqrt {\dfrac{{2H}}{g}}$
Substituting the given values in the above equation we get
$t = \sqrt {\dfrac{{2 \times 490}}{{10}}}$
$\Rightarrow t = 7\sqrt 2$
We know that since the bomb will cover the horizontal distance which can be calculated by the formula $\text{distance = speed} \times \text{time}$.

\therefore \text{distance}= 420\sqrt 2 m$$. **Hence, the total horizontal distance traveled by the packet is $420\sqrt 2 m$.** **Note:** In the above question we used the terms “distance and displacement” there is so much difference between both terms which can be explained as distance represents the total measurement of the path followed by any object whereas displacement is the measurement of the smallest path followed by the object a displacement of a body can be negative whereas distance can’t be negative, distance is a vector quantity whereas the displacement is a vector quantity.