Would someone please show me a way to work this out

A ball is dropped from the top of a building 150 m high. (Ignore air resistance)
A. How long does it take the ball to hit the ground?

B. What is the speed of the ball when it hits the ground?

To calculate the time it takes for the ball to hit the ground, we can use the kinematic equation:

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

where h is the height of the building (150 m), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time in seconds. We need to solve for t.

Step 1: Rearrange the equation to solve for t.
Start by multiplying both sides of the equation by 2:
2h = g * t^2.

Step 2: Divide both sides of the equation by g.
t^2 = (2h) / g.

Step 3: Take the square root of both sides of the equation.
t = √((2h) / g).

Now we can substitute the given values into the equation to find the time (t).

A. How long does it take the ball to hit the ground?
t = √((2 * 150) / 9.8)
t = √(300 / 9.8)
t ≈ 5.43 seconds.

Therefore, it takes approximately 5.43 seconds for the ball to hit the ground.

To calculate the speed of the ball when it hits the ground, we can use another kinematic equation:

v = g * t,

where v is the velocity of the ball and remains constant during free fall.

B. What is the speed of the ball when it hits the ground?
v = g * t
v = 9.8 m/s^2 * 5.43 s
v ≈ 53.3 m/s.

Therefore, the speed of the ball when it hits the ground is approximately 53.3 m/s.