To find the time it takes for the ball to reach the plane of the fence, we can use the horizontal component of the velocity.
First, we need to find the horizontal component of the initial velocity. Given that the initial velocity is 17 m/s and the angle above the horizontal is 45 degrees, we can use trigonometry to find the horizontal component:
horizontal velocity = initial velocity * cos(angle)
horizontal velocity = 17 m/s * cos(45 degrees)
horizontal velocity ≈ 17 m/s * 0.707 ≈ 12.02 m/s
Now we can use the equation for horizontal motion to find the time it takes for the ball to reach the fence:
horizontal distance = horizontal velocity * time
20 m = 12.02 m/s * time
time ≈ 20 m / 12.02 m/s ≈ 1.663 s
Therefore, it takes approximately 1.663 seconds for the ball to reach the plane of the fence.
To find how far above the top of the fence the ball will pass, we can use the vertical component of the velocity and the time it takes to reach the fence.
First, we need to find the vertical component of the initial velocity. Given that the initial velocity is 17 m/s and the angle above the horizontal is 45 degrees, we can use trigonometry to find the vertical component:
vertical velocity = initial velocity * sin(angle)
vertical velocity = 17 m/s * sin(45 degrees)
vertical velocity ≈ 17 m/s * 0.707 ≈ 12.02 m/s
Now we can use the equation for vertical motion to find the distance above the top of the fence:
vertical distance = vertical velocity * time - (1/2) * acceleration due to gravity * time^2
vertical distance = 12.02 m/s * 1.663 s - (1/2) * 9.8 m/s^2 * (1.663 s)^2
vertical distance ≈ 19.95 m - 17.373 m ≈ 2.577 m
Therefore, the ball will pass approximately 2.577 meters above the top of the fence.
To find the vertical component of the velocity when the ball reaches the plane of the fence, we can use the acceleration due to gravity and the time it takes to reach the fence.
Using the equation for vertical motion, we can find the vertical component of the velocity:
vertical velocity at the fence = vertical velocity - acceleration due to gravity * time
vertical velocity at the fence = 12.02 m/s - 9.8 m/s^2 * 1.663 s
vertical velocity at the fence ≈ 12.02 m/s - 16.25 m/s ≈ -4.23 m/s
Therefore, the vertical component of the velocity when the ball reaches the plane of the fence is approximately -4.23 m/s, indicating that the ball is moving downward.