<h2>
Answer:</h2>
9.86s
<h2>
Explanation:</h2>
The total time ( ) the ball is in flight is the sum of the time taken (
) the ball is in flight is the sum of the time taken ( ) to reach maximum height and the time taken (
) to reach maximum height and the time taken ( ) to strike the ground from maximum height. i.e
) to strike the ground from maximum height. i.e
 =
 =  +
 + 
<em>Calculate time taken to reach maximum height, </em> .
.
Using one of the equations of motion;
v = u + at   ------------------------(i)
Where;
v = final velocity of the ball = 0 (at maximum height, velocity is zero (0));
u = initial velocity of the ball = 42.4m/s
a = acceleration due to gravity = g = -10m/s² ( this is negative since the ball is thrown upwards against the direction of gravity)
t = time taken to reach maximum height = 
Substitute these values into equation (i) as follows;
0 = 42.4 - 10( )
)
 = 42.4 / 10
 = 42.4 / 10
 = 4.24s
 = 4.24s
<em>The time taken (</em> <em>)to reach maximum height = 4.24s</em>
<em>)to reach maximum height = 4.24s</em>
<em />
<em>Calculate the time taken to strike the ground from maximum height, </em> <em />
<em />
(i) First let's get the maximum height reached relative to the roof of the building using another equation of motion;
h = ut +  x a
 x a --------------------------(ii)
      --------------------------(ii)
Where;
h = maximum height;
u = initial velocity of the ball = 42.4m/s
a = -10m/s² ( this is negative since the ball is thrown upwards against the direction of gravity)
t = time taken to reach maximum height = 4.24s
Substitute these values into equation (ii) as follows;
=> h = (42.4 x 4.24) -  x 10 x 4.24²
 x 10 x 4.24²
=> h = 179.776 - 89.888
=> h = 89.888m
(ii) Second, let's find the time taken to strike the ground from maximum height using the same equation (ii);
Where;
h = total height relative to the ground = maximum height + building height
h = 89.888 + 68.1 = 157.988m
u = initial velocity from maximum height = 0 (at maximum height, velocity is 0)
a = acceleration due to gravity = +10m/s² (this is positive since the ball now moves downwards in the direction of gravity)
t = time taken from maximum height to strike the ground = 
Substitute these values into equation(ii);
157.988 = 0( ) +
) +  x 10 x
 x 10 x  ²
²
157.988 = 5 ²
²
Solve for  ;
;
 ² = 157.988 / 5
² = 157.988 / 5
 ² = 31.60
² = 31.60
 =
 = 
 = 5.62s
 = 5.62s
Therefore, time taken to strike the ground from maximum height is 5.62s
<em>Calculate the total time in air, </em> <em></em>
<em></em>
 =
 =  +
 + 
 = 4.24 + 5.62
 = 4.24 + 5.62
 = 9.86s
 = 9.86s
The total time the ball is in flight is 9.86s