A boy is playing a ball in a garden surrounded by a wall 2.5 m high and kicks the ball vertically up from a height of 0.4 m with a speed of 14 m/s . For how long is the ball above the height of the wall.

2.5 sec

Step-by-step explanation:

Height of wall = 2.5 m

initial speed of ball = 14 m/s

height from which ball is kicked = 0.4 m

we calculate the speed of the ball at the height that matches the wall first

height that matches wall = 2.5 - 0.4 = 2.1 m

using  =  + 2as

where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)

=  + 2(-9.81 x 2.1)

= 196 - 41.202

= 154.8

v =  = 12.44 m/s

this is the velocity of the ball at exactly the point where the wall ends.

At the maximum height, the speed of the ball becomes zero

therefore,

u = 12.44 m/s

v = 0 m/s

a = -9.81 m/s^2

t = ?

using V = U + at

0 = 12.44 - 9.81t

-12.44 = -9.81

t = -12.44/-9.81

t = 1.27 s

the maximum height the ball reaches will be gotten with

=  + 2as

a = -9.81 m/s^2

0 =  + 2(-9.81s)

0 = 196 - 19.62s

s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.

height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m

we calculate for the time taken for the ball to travel down this height

a = 9.81 m/s^2 (positive in downwards movement)

u = 0

s = 7.49 m

using s = ut + a

7.49 = (0 x t) +  (9.81 x  )

7.49 = 0 + 4.9

 = 7.49/4.9 = 1.53

t =  = 1.23 sec

Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec

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step-by-step explanation: