A man stands on the roof of a building that is 50 m tall and throws a rock with a velocity of 35 m/s at an angle of 50 degrees above the horizontal

(a) What is the total time in the air
(b) What is the horizontal distance from the base of the building to the point where the rock strikes the ground
(c) What is the maximum height above the building
(d) What is the velocity of the rock just before it hit the ground

See 3:47 AM post.

To solve these questions, we need to use equations of motion and kinematic principles. Let's go through each question step by step:

(a) To find the total time in the air, we can use the vertical motion equation:

h = ut + (1/2)gt^2

where:
h = height (50 m)
u = initial vertical velocity (35 m/s * sin(50°))
g = acceleration due to gravity (-9.8 m/s^2)
t = time

Rearranging the equation to solve for t, we have:

t = (2h / g)^(1/2)

Substituting the given values, we can calculate the total time in the air.

(b) To find the horizontal distance from the base of the building to the point where the rock strikes the ground, we can use the horizontal motion equation:

x = ut + (1/2)gt^2

where:
x = horizontal distance
u = initial horizontal velocity (35 m/s * cos(50°))
g = 0 m/s^2 (since there is no acceleration in the horizontal direction)
t = time (which we calculated in part (a))

Substituting the given values, we can calculate the horizontal distance.

(c) The maximum height above the building can be found using the equation:

h_max = (u^2 * sin^2(theta)) / (2g)

where:
h_max = maximum height above the building
u = initial velocity of the rock (35 m/s)
theta = angle of projection (50°)
g = acceleration due to gravity (-9.8 m/s^2)

Substituting the given values, we can calculate the maximum height.

(d) To find the velocity of the rock just before it hits the ground, we can use the equation:

v = u + gt

where:
v = final velocity (just before it hits the ground)
u = initial velocity of the rock (35 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = total time in the air (calculated in part (a))

Substituting the given values, we can calculate the final velocity.

Now, with the equations and steps outlined, you can use these formulas and the given values to find the answers to each question.