Question

A ball is thrown with an initial velocity of 20 $m{s}^{-1}$. Find the time of flight and the maximum height reached by the body. (g = 10 $m{s}^{-2}$)

• A. 4 s and 20 m
• B. 5 s and 25 m
• C. 6 s and 36 m
• D. 7 s and 49 m

Answer 1

The correct option is A

4 s and 20 m

The acceleration due to gravity is opposite to the motion. At some point of motion, velocity will become zero. At that moment, the ball will change the direction of motion and fall downwards. Thus at maximum height, velocity will be zero.
Since, acceleration of gravity is opposite to motion, a = -10 $m{s}^{-2}$, final velocity v= 0, initial velocity u = 20 $m{s}^{-1}$​​​​​​​
From, v = u + at
0 = 20+ (-10) t
t = 2 s
Thus the ball takes 2 s to reach the top. Similarly to reach the ground from the top point is also 2 s. Thus total time or time of flight is 4 s.
s = ut + $\frac{1}{2}$ a$t^2$
s = 20 $\times$ 2 + $\frac{1}{2}$ (-10) $\times$ $2^2$ = 20 m