A punter kicks a football with a certain initial velocity of 13.8 m/s at an angle of 20.0o above the horizontal. How long does it take the ball to rise to the highest point of its tragetory?
To find the time it takes for the ball to reach the highest point of its trajectory, we can make use of the vertical component of its initial velocity.
Given:
Initial velocity (v) = 13.8 m/s
Angle above horizontal (θ) = 20.0°
Step 1: Calculate the vertical component of the initial velocity (v_y):
v_y = v * sin(θ)
= 13.8 * sin(20.0°)
≈ 4.70 m/s
Step 2: Use the vertical component of the initial velocity to calculate the time (t) it takes for the ball to reach the highest point of its trajectory. The formula is as follows:
t = v_y / g
where g is the acceleration due to gravity, approximately 9.8 m/s².
t = 4.70 / 9.8
≈ 0.48 seconds
Therefore, it takes approximately 0.48 seconds for the ball to rise to the highest point of its trajectory.
To find the time it takes for the ball to reach the highest point of its trajectory, we can use the formula for the vertical component of the motion:
vf = vi + at
Where vf is the final vertical velocity (which becomes 0 at the highest point), vi is the initial vertical velocity, a is the acceleration (in this case, the acceleration due to gravity, which is approximately -9.8 m/s^2), and t is the time.
At the highest point, the final vertical velocity is 0. Therefore, we can rearrange the formula to solve for time:
0 = vi + (-9.8)t
Rearranging the formula further:
-9.8t = -vi
Dividing both sides by -9.8:
t = vi / 9.8
Now, we can substitute the given values into the formula:
vi = 13.8 m/s
t = 13.8 / 9.8
t ≈ 1.41 seconds
Therefore, it takes approximately 1.41 seconds for the ball to rise to the highest point of its trajectory.