A football player kicks with a speed of 21 m/s at 37 degree to the horizontal. How long is the ball in the air?
initial speed up Vi = 21 sin 37
v = Vi - 9.81 t
at top v = 0
so
t = ( 21 sin 37 ) / 9.81 = time rising
time falling = time rising
so
2 t = time in air
To find out how long the ball is in the air, we can use the concept of projectile motion. We need to separate the motion into horizontal and vertical components.
First, let's find the time it takes for the ball to reach the highest point of its trajectory (when it is not moving up or down). At this point, the vertical component of the velocity becomes zero.
Step 1: Calculate the vertical component of the initial velocity (vₒ) using trigonometry.
vₒy = vₒ * sin(θ)
vₒy = 21 m/s * sin(37°)
vₒy ≈ 12.59 m/s
Step 2: Apply the formula to find the time it takes to reach the highest point. The formula is:
t = vₒy / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
t ≈ 12.59 m/s / 9.8 m/s²
t ≈ 1.28 s
Now that we have the time it takes to reach the highest point, we can use it to find the total time of flight. Since the motion is symmetrical, the time of flight is twice the time it took to reach the highest point.
Step 3: Calculate the total time of flight (T).
T = 2 * t
T = 2 * 1.28 s
T ≈ 2.56 s
Therefore, the ball is in the air for approximately 2.56 seconds.