A golf ball is shot from a tee, elevated 20m above the green, with an initial speed of 27m/s at an angle of 50° above horizontal.

a) What will be the speed of the golf ball before it hits the green, 20m below it started?
b) How much time will it take for the ball to travel from the tee, where it is shot to the green?
c) What horizontal distance will the ball travel in moving from the shot at the tee to hitting the green?

If you are not familiar with the equations for trajectories, the wikipedia article for that subject has a good treatment. Just plug in your values for the equation of motion, and crank it out.

If you get stuck, come on back with your work so far, and we can give you a nudge in the right direction.

I'm not familiar with the equations.

To answer these questions, we can use the equations of motion in projectile motion. Let's break down each question and explain how to solve it using these equations:

a) What will be the speed of the golf ball before it hits the green, 20m below where it started?

To find the speed of the ball before it hits the green, we need to find the vertical component of its velocity at that point. We can use the equation:

v_final = v_initial + (a * t)

where:
v_final is the final velocity,
v_initial is the initial velocity,
a is the acceleration (in this case, due to gravity, which is -9.8 m/s^2),
t is the time.

Since the golf ball is moving vertically and downard, the final velocity in the vertical component will be negative, as the ball is falling.

The initial vertical velocity can be found using the equation:

v_initial_vertical = v_initial * sin(angle)

where:
v_initial is the initial velocity,
angle is the angle above horizontal.

Given that v_initial = 27 m/s and angle = 50°, we can calculate:

v_initial_vertical = 27 m/s * sin(50°)
v_initial_vertical ≈ 21.85 m/s

Now we can find the time it takes for the ball to reach the green using the equation:

20 m = v_initial_vertical * t + (1/2) * a * t^2

Substituting the known values:

20 m = (21.85 m/s) * t + (1/2) * (-9.8 m/s^2) * t^2

Simplifying the equation yields a quadratic equation, which we can solve to find the time it takes for the ball to reach the ground.

b) How much time will it take for the ball to travel from the tee to the green?

We already have the equation above, which we can solve to find the time (t) it takes for the ball to reach the green.

c) What horizontal distance will the ball travel in moving from the shot at the tee to hitting the green?

To find the horizontal distance traveled by the ball, we can use the equation:

horizontal_distance = v_horizontal * t

where:
v_horizontal is the horizontal component of the initial velocity, given by:

v_initial_horizontal = v_initial * cos(angle)

Using the known values (v_initial = 27 m/s and angle = 50°), we can calculate:

v_initial_horizontal = 27 m/s * cos(50°)
v_initial_horizontal ≈ 17.36 m/s

We already know the time it takes for the ball to reach the green from part b), so we can calculate the horizontal distance using the formula above.