A woman throws a ball at a vertical wall d = 4.8 m away. The ball is h = 2.4 m a

Question

A woman throws a ball at a vertical wall d = 4.8 m away. The ball is h = 2.4 m above ground when it leaves the woman's hand with an initial velocity of 13 m/s at 45°. When the ball hits the wall, the horizontal component of its velocity is reversed; the vertical component remains unchanged. (Ignore any effects due to air resistance.)

(a) Where does the ball hit the ground?

____________________________m (away from the wall)

(b) How long was the ball in the air before it hit the wall?
____________________________ s

(c) Where did the ball hit the wall?
_______________________ m (above the ground)

(d) How long was the ball in the air after it left the wall?

___________________________s

Explanation / Answer

Initial height of Ball = 2.4 m
Velocity = 13m/s @ 45o

Vx = 13 cos(45) = 9.2 m/s
Vy = 13 sin(45) = 9.2m/s

Acceleration in x direction = 0
Acceleration in y direction = 9.8 m/s^2 (downwards)

Horizontal distance = 4.8m
Time taken by ball to cover this distance =
s = u*t
4.8 = 9.2 * t
t = 0.52 s
Ball in the air before it hit the wall t = 0.52 s

Distance travelled in Y direction =
S = ut - 0.5*g*t^2
S = 9.2 * 0.52 - 0.5 *9.8*0.52^2
S = 3.45 m
Total Height Reached by ball = 3.45m + 2.4m

Ball hit the wall at S = 5.85m

Vertical Velocity when ball hits the wall = 9.2m/s - 9.8 * 0.52 = 4.1m/s
Now,
Total time taken by ball to reach highest point =
V = u + at
0 = 9.2 - 9.8 * t1
t1 = 9.2/9.8 = 0.94s

Vertical height reached =
S = 9.2 * 0.94 - 0.5 * 9.8 *0.94^2
S = 4.32 m

Total hegiht = 4.32 + 2.4 = 6.72m
S = 0.5 *9.8 * t^2
t =sqrt(6.72/4.9) =1.2s

Time ball was in the air after it left the wall = 0.94s -0.52s+ 1.2s
Time ball was in the air after it left the wall = 1.62s

Horizontal distance travelled in 1.62s = 9.2 * 1.62 = 14.9 m
Ball hits the Ground  14.9 m away from the wall.

a) Ball hits the Ground  14.9 m away from the wall.
b) Ball was in the air before it hit the wall t = 0.52 s.
c) Ball hit the wall at S = 5.85m.
d) Time ball was in the air after it left the wall = 1.62s.

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