Question

With what speed in $milesh{r^{ - 1}}$ ( $1m{\sec ^{ - 1}} = 2.23\,milesh{r^{ - 1}}$ ) must an object be thrown to reach a height of $91.5\,m$ (equivalent to one football field)? Assume negligible air resistance.
A. $94.4\,milesh{r^{ - 1}}$
B. $84.4\,milesh{r^{ - 1}}$
C. $74.4\,milesh{r^{ - 1}}$
D. $94\,milesh{r^{ - 1}}$

Answer 1

Hint: In order to solve this question we need to understand force of gravity. Force of gravity is defined as force which acts in downward direction due to the space curve of earth. Due to this force an acceleration produced in body in downward direction knows as acceleration due to gravity having magnitude of, $g = 9.8m{\sec ^{ - 2}}$ also the air resistance plays an important factor as it increases with speed of body and also it depends on the surface area of falling object.

Complete step by step answer:
Let us assume that the body thrown vertically upwards with initial speed,
$u = x$ $m{\sec ^{ - 1}}$
Height it can reach is, $s = h = 91.5\,m$.
Since we know, acceleration due to gravity is given by, $a = - g = 9.8\,m{\sec ^{ - 2}}$.
Since the acceleration is constant we can use the equation of motion, also at the height point the object would be at rest so the final speed of the body is $v = 0\,m{\sec ^{ - 1}}$.
Using third equation of motion we get,
${v^2} = {u^2} + 2as$
Putting values we get, $0 = ({x^2}) - 2(g)(h)$
${x^2} = 2gh$
$\Rightarrow {x^2} = 2 \times 9.8 \times 91.5\,{m^2}{\sec ^{ - 2}}$
$\Rightarrow {x^2} = 1793.40\,{m^2}{\sec ^{ - 2}}$
$\Rightarrow x = 42.348\,m\,{\sec ^{ - 1}}$
Or in miles we get, $x = 42.348 \times 2.23\,miles\,h{r^{ - 1}}$ as $1m\,{\sec ^{ - 1}} = 2.23\,miles\,h{r^{ - 1}}$
$\therefore x = 94.43\,miles\,h{r^{ - 1}}$

So the correct option is A.

Note: It should be remembered that here we have neglected air resistance while calculation so as to make the problem easy, but the air resistance is important factor as due to this we can play football in rains but we cannot play in ground if someone throws a penny from a building on us. Because upon downfall of rain it is acted by force of gravity and thereby increasing its speed but as the speed increases air resistance also increases, so after some time force due to air resistance becomes equal to force of gravity in opposite direction so the falling raindrop maintained at constant speed and hence when it comes down on our head we do not feel that much force.