A golfer is attempting to hit the ball onto an 18m green over a gorge. The location

where the ball is hit from is elevated 35m above the green which is 65m away.
Assume the ball was hit at a velocity of 20m/s at 40 degrees: Questions:

1. does the ball land on the green and why?
2. What is the max speed of the ball?
3. What is the maximal height the ball reaches?

Vo = 20m/s[40o] Above the hor.?

Xo = 20*Cos40 = 15.32 m/s.
Yo = 20*sin40 = 12.86 m/s.

1. Y^2 = Yo^2 + 2g*h = 0
h = 35 + -(Yo^2)/2g
h = 35 + -(12.86^2)/-19.6 = 43.44 m Above the green.

Y = Yo + g*Tr = 0
Tr = -Yo/g = -12.86/-9.8 = 1.31 s. = Rise time.

h = 0.5g*t^2 = 43.44
4.9t^2 = 43.44
t^2 = 8.87
t = 2.98 s. = Fall time(Tf). = Time to
fall to the green.

Dx = Xo*(Tr+Tf)=15.32m/s * (1.31+2.98)s=
65.7 m. = The required hor. distance.
Therefore, the ball lands on the green.

2. Y = Yo + g*Tf = 0 + 9.8 * 2.98 = 29.2
m/s. = Ver. component.

V = sqrt(Xo^2+Y^2)
Xo = 15.32 m/s
Y = 29.2 m/s
Solve for V.

3. h max = 43.44 m. Above the green(Prob. #1).

To answer these questions, we need to break down the problem into different components and use basic physics equations related to projectile motion. Here's how you can find the answers:

1. Will the ball land on the green?

To determine if the ball will land on the green, we need to calculate the horizontal distance traveled by the ball. We can use the formula:

Horizontal distance = initial velocity * cosine(angle) * time

In this case, the initial velocity is 20m/s, the angle is 40 degrees, and the time can be found using the formula:

time = (2 * initial velocity * sine(angle)) / gravitational acceleration

Since the gravitational acceleration is approximately 9.8 m/s^2, we can substitute these values into the equations and calculate the time and horizontal distance. If the horizontal distance is less than or equal to 65m (the distance to the green), the ball will land on the green.

2. What is the maximum speed of the ball?

To find the maximum speed of the ball, we need to calculate the magnitude of the velocity vector at its peak height. The vertical velocity component at its peak (before it starts descending) will be zero, and the only velocity will be the horizontal component.

The horizontal velocity component can be calculated using the formula:

Horizontal velocity = initial velocity * cosine(angle)

This means that the maximum speed of the ball is equal to the horizontal velocity component, which can be found by substituting the given values into the equation.

3. What is the maximum height the ball reaches?

To find the maximum height, we need to calculate the vertical distance achieved by the ball. We can use the formula:

Vertical distance = (initial velocity * sine(angle))^2 / (2 * gravitational acceleration)

By substituting the given values into the equation, you can find the maximum height reached by the ball.

Keep in mind that these calculations assume ideal conditions, neglecting factors like air resistance. Also, it's important to use appropriate unit conversions if necessary.