A ball of mass 0.4 kg, initially at rest, is kicked directly toward a fence from a point 20 m away, as shown below.

The velocity of the ball as it leaves the kicker's foot is 17 m/s at angle of 35 degree above the horizontal. The top of the fence is 3 m high. The ball hits nothing while in flight and air resistance is negligible.
The acceleration due to gravity is 9.8 m/s^
Determine the time it takes for the ball to reach the plane of the fence.
Answer in units of s.

Part One of Three

Dx=20 meters
Dy=3 meters (Don't need to know that for this part of the question)
g=-9.8 m/s^2
Vix=17 m/s
Vi in this formula is cos(35)*17
Formula: Dx=Vit
20=cos(35)*17
20=13.93t
20/13.93= 1.44
T=1.44 seconds!

Part Two of Three
Viy=sin(35)*17=9.75 m/s
T (found in Part 1 of 3)=1.44 seconds
Dy=3 meters (not needed until end of problem)
a=g or (-9.8 m/s^2)
Formula Used: Dy=Viyt+1/2at^2
Ignore Dy value of 3 for now
Dy=9.75*1.44+1/2(-9.8)1.44^2
Dy=14.04-10.16=3.88
Now dy=3 meters
3.88-3=0.88 meters above the fence.

Part Three of Three
Formula Used= Vfy=Viy+ay*t
Viy=9.75
A=-9.8m/s^2 or g
T=1.44 seconds
Vfy=9.75+(-9.8)*1.44
-(negative)*+(positive)=-(negative)
Vfy=9.75-14.11
Vfy=-4.36

How far above the top of fence will the ball pass? Consider the diameter of the ball to be negligible.

Answer in units of m.

What is the vertical component of the velocity when the ball reaches the plane of the fence?
Answer in units of m/s.

Well, let's see... a ball's journey toward a fence. It sounds like it's really trying to make a point!

To find the time it takes for the ball to reach the plane of the fence, we can break down its motion into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component is affected by gravity.

First, let's find the horizontal distance the ball travels. Using the initial velocity of 17 m/s at an angle of 35 degrees above the horizontal, we can find the horizontal component of the initial velocity:

Vx = 17 m/s * cos(35°)

Next, we can use the formula for horizontal distance:

dx = Vx * t

Where dx is the horizontal distance and t is the time.

Given that the horizontal distance is 20 m, we can set up the equation:

20 m = (17 m/s * cos(35°)) * t

Now, let's solve for t:

t = 20 m / (17 m/s * cos(35°))

t ≈ 0.816 s

So, it takes approximately 0.816 seconds for the ball to reach the plane of the fence. Keep on kicking those questions, I'm here to entertain!

To determine the time it takes for the ball to reach the plane of the fence, we can analyze the motion of the ball both horizontally and vertically.

First, we'll split the initial velocity of the ball into its horizontal and vertical components.

Vertical component of the initial velocity, Vy = V * sin(theta)
Horizontal component of the initial velocity, Vx = V * cos(theta)

Given:
- Velocity, V = 17 m/s
- Angle, theta = 35 degrees

We can calculate the vertical and horizontal components of the initial velocity as follows:

Vy = 17 m/s * sin(35 degrees)
Vy = 17 m/s * 0.574
Vy ≈ 9.764 m/s

Vx = 17 m/s * cos(35 degrees)
Vx = 17 m/s * 0.819
Vx ≈ 13.923 m/s

Now, we'll determine the time it takes for the ball to reach the plane of the fence using the vertical motion of the ball.

The vertical motion is affected by acceleration due to gravity, which is acting downwards. The initial vertical velocity is positive because it is directed upwards. At the highest point of its trajectory, the vertical velocity is 0 m/s.

Using the formula for vertical displacement, s = u*t + (1/2)*a*t^2, where:
- s = vertical displacement (height of the fence) = 3 m
- u = initial vertical velocity = 9.764 m/s
- a = acceleration due to gravity = -9.8 m/s^2 (negative because it's acting downwards)
- t = time

We can rewrite the formula as follows:

0 = 9.764 m/s * t + (1/2) * (-9.8 m/s^2) * t^2

Simplifying the equation:

-4.9 * t^2 + 9.764 * t = 0

Now, we can solve the above equation for t using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where:
a = -4.9
b = 9.764
c = 0

Plugging in the values:

t = (-9.764 ± √(9.764^2 - 4 * -4.9 * 0)) / (2 * -4.9)
t = (-9.764 ± √(95.361296 - 0)) / -9.8
t = (-9.764 ± √95.361296) / -9.8

Now, we can compute the two possible values for t and choose the positive value since time cannot be negative:

t1 = (-9.764 + √95.361296) / -9.8
t1 ≈ 1.018 s

t2 = (-9.764 - √95.361296) / -9.8 (this value is ignored since it's negative)

Therefore, the time it takes for the ball to reach the plane of the fence is approximately 1.018 seconds.

To determine the time it takes for the ball to reach the plane of the fence, we can first find the vertical component of the initial velocity, and then use the kinematic equation for vertical motion.

1. Find the vertical component of the initial velocity (Vy).
According to the given information, the initial velocity of the ball is 17 m/s at an angle of 35 degrees above the horizontal. The vertical component of this velocity (Vy) can be found using trigonometry:
Vy = V * sin(theta)
Vy = 17 m/s * sin(35 degrees)
Vy ≈ 17 m/s * 0.574
Vy ≈ 9.798 m/s (approximated to three decimal places)

2. Use the kinematic equation for vertical motion to find the time it takes for the ball to reach the plane of the fence.
The kinematic equation for vertical motion in the presence of gravity is:
h = Vy * t + (1/2) * g * t^2
where:
h = vertical displacement (height of the fence = 3 m)
Vy = vertical component of initial velocity (9.798 m/s)
t = time
g = acceleration due to gravity (-9.8 m/s^2, as it acts downward)

Substituting the given values into the equation:
3 m = (9.798 m/s) * t + (1/2) * (-9.8 m/s^2) * t^2

3. Solve the equation to find the time.
Rearranging the equation and putting it into quadratic form:
(1/2) * (-9.8 m/s^2) * t^2 + (9.798 m/s) * t - 3 m = 0

Solve this quadratic equation to find the time using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / (2a)

where:
a = (1/2) * (-9.8 m/s^2)
b = (9.798 m/s)
c = -3 m

Plugging in the values into the quadratic formula and solving:
t = [-(9.798 m/s) ± sqrt((9.798 m/s)^2 - 4 * (1/2) * (-9.8 m/s^2) * (-3 m))] / (2 * (1/2) * (-9.8 m/s^2))
t = [-(9.798 m/s) ± sqrt(96.02 m^2/s^2)] / (-9.8 m/s^2)
t = [-(9.798 m/s) ± 9.799 m/s] / (-9.8 m/s^2)

We have two solutions, so let's calculate both separately:
Solution 1: t = (-(9.798 m/s) + 9.799 m/s) / (-9.8 m/s^2)
Solution 2: t = (-(9.798 m/s) - 9.799 m/s) / (-9.8 m/s^2)

Calculating Solution 1:
t = (0.001 m/s) / (-9.8 m/s^2)
t ≈ -0.0001 s (Ignoring the negative value since time cannot be negative)

Calculating Solution 2:
t = (-19.597 m/s) / (-9.8 m/s^2)
t ≈ 2 s (approximated to one decimal place)

Therefore, the time it takes for the ball to reach the plane of the fence is approximately 2 seconds.