Ballkicked from ground at initial speed 19.5m/s at upward angle 45°.a player 55m awayinthe directionofkick startsrunning tomeet theball atthat instantwhat isaverage speedmeet beforeballhit the ground?

To find the average speed at which the player meets the ball before it hits the ground, we first need to find the time it takes for the ball to hit the ground.

The vertical motion of the ball can be analyzed using the equation:

y = y0 + v0yt - 0.5gt^2

where:
y = final vertical position (0, since the ball hits the ground)
y0 = initial vertical position (0)
v0y = initial vertical velocity (19.5sin(45°) m/s)
g = acceleration due to gravity (9.81 m/s^2)
t = time

Plugging in the values, we get:

0 = 0 + 19.5sin(45°)t - 0.5*9.81*t^2
0 = 13.78t - 4.905t^2
4.905t^2 - 13.78t = 0
t(4.905t - 13.78) = 0

This gives us two possible solutions for t: t = 0 (initial time) and t = 2.81 seconds.

Now, we need to find the horizontal distance the ball travels in 2.81 seconds:

x = v0x*t
x = 19.5cos(45°)*2.81
x = 31.05 meters

Since the player starts running from 55 meters away, the player needs to cover 55 - 31.05 = 23.95 meters in 2.81 seconds to meet the ball.

Therefore, the average speed at which the player meets the ball before it hits the ground is:

Average speed = total distance / total time
Average speed = 23.95 meters / 2.81 seconds
Average speed ≈ 8.52 m/s

Step 1: Calculate the time of flight of the ball

Vertical Motion:

- Initial vertical velocity: v0y = 19.5 m/s - sin(45°) = 13.84 m/s
- Acceleration due to gravity: g = 9.81 m/s^2

Using the equation: v = u + at
vf = 0
u = 13.84 m/s
a = -9.81 m/s^2
0 = 13.84 - 9.81t
t = 1.41 s

Horizontal Motion:

- Initial horizontal velocity: v0x = 19.5 m/s - cos(45°) = 13.84 m/s
- Displacement: x = 55 m

Using the equation: x = ut + 0.5at^2
x = 13.84 - 1.41 + 0.5 - 0 - 1.41^2
x = 19.49 m

Therefore, the time of flight of the ball is 1.41 s, and it covers a horizontal distance of 19.49 m before hitting the ground.

Step 2: Calculate the average speed of the player

- Distance covered by the player: 55 m - 19.49 m = 35.51 m
- Time taken by the player: 1.41 s

Average Speed:

Average speed = Distance / Time
Average speed = 35.51 m / 1.41 s
Average speed = 25.18 m/s

Therefore, the average speed of the player before the ball hits the ground is 25.18 m/s.