A projectile is kicked horizontally off a tall building with an initial velocity of 13.7 m/s. The projectile lands 56.2 m away from the base of the building. How long is the projectile in the air? How tall is the building? What is the velocity of the projectile when it strikes the ground?

u = 13.7

t = 56.2/13.7 seconds in air

h = .5 g t^2 for height

v = g * t vertical + 13.7 horizontal

To find the time the projectile is in the air, we can use the horizontal distance it travels and the initial horizontal velocity.

Step 1: Determine the time of flight
The horizontal distance traveled by the projectile is 56.2 m, and the initial horizontal velocity is 13.7 m/s. Since the initial vertical velocity is zero (since the projectile is kicked horizontally), we can use the formula:

distance = velocity × time

Rearranging the formula to solve for time:

time = distance / velocity

Plugging in the values, we get:

time = 56.2 m / 13.7 m/s = 4.1 seconds

So, the projectile is in the air for 4.1 seconds.

To find the height of the building, we can use the time of flight and the acceleration due to gravity.

Step 2: Determine the height of the building
Since we know the time of flight of the projectile, we can use the formula:

height = (acceleration due to gravity × time^2) / 2

The acceleration due to gravity is approximately 9.8 m/s^2. Plugging in the values, we get:

height = (9.8 m/s^2 × (4.1 s)^2) / 2 = 82.58 m

So, the height of the building is approximately 82.58 meters.

To find the velocity of the projectile when it strikes the ground, we can use the time of flight and the acceleration due to gravity.

Step 3: Determine the velocity of the projectile when it strikes the ground
Using the formula for the final velocity:

final velocity = initial velocity + (acceleration due to gravity × time)

The initial vertical velocity is zero (as the projectile is kicked horizontally), and the acceleration due to gravity is 9.8 m/s^2. Plugging in the values, we get:

final velocity = 0 + (9.8 m/s^2 × 4.1 s) = 40.18 m/s

So, the velocity of the projectile when it strikes the ground is approximately 40.18 m/s.