To calculate the time of flight, we first need to break down the initial velocity into its horizontal and vertical components.
Horizontal component of velocity (Vx) = 20 m/s * cos(31°)
Vx = 20 m/s * 0.857 = 17.14 m/s
Vertical component of velocity (Vy) = 20 m/s * sin(31°)
Vy = 20 m/s * 0.529 = 10.58 m/s
Next, we can use the vertical component of velocity to calculate the time it takes for the ball to reach the highest point of its trajectory. We can use the equation:
Vy = Voy - gt
where
Voy = initial vertical velocity = 10.58 m/s
g = acceleration due to gravity = 9.81 m/s^2
t = time
0 = 10.58 - 9.81t
t = 10.58 / 9.81
t = 1.08 seconds
Since the time of flight is the total time it takes for the ball to travel up and then back down to the same height, we can double the time it takes to reach the highest point:
Time of flight = 2 * 1.08 seconds
Time of flight = 2.16 seconds
Therefore, the time of flight of the ball is 2.16 seconds.
A goalkeeper kicks the ball from his goal area at a velocity of 20 m/s and at an angle of 31° to the horizontal. Calculate: 4.1 The time of flight
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