Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# The friction of the air causes vertical retardation equal to one-tenth of the acceleration due to gravity (take $g=10\;ms^{-1}$). Find the decrease in the time of flight. (in percent)a). 9b). 10c). 11d). 8

Last updated date: 14th Apr 2024
Total views: 33.6k
Views today: 0.33k
Verified
33.6k+ views
Hint: Assume throwing a ball vertically upwards and then find its time of flight in both with or without retardation due to the air using equations of motion. Then once we get both the time of flights, we can find the percentage increase or decrease in the time of flight by calculating the change.

Let us assume a ball is thrown vertically upwards with a velocity $u$, then at the maximum height, the velocity of the ball will become zero. Considering there is no retardation caused due to air then by using equation of motion $v = u + at$, where $v$ is the final velocity of ball at the maximum height, $u$ is the initial velocity, $a$ is the acceleration due to gravity and $t$ be the time of flight.
So, we can write, $0=u–gt\implies t = \dfrac{u}{g}$ ………. (i)
Therefore, effective acceleration $g’=g+\dfrac{g}{10}=\dfrac{11g}{10}$
Now, the time of flight, $T’=\dfrac{u}{\dfrac{11g}{10}}=\dfrac{10u}{11g}$ ………. (ii)
Thus, change in time of flight $=\delta T=T-T’=\dfrac{u}{g}-\dfrac{10u}{11g}=\dfrac{u}{11g}$
The percentage change in the time of flight $=\dfrac{\delta T}{T}\times 100\%=\dfrac{\dfrac{u}{11g}}{\dfrac{u}{g}}\times 100\%=\dfrac{100}{11} \% =9\%$