A ball is thrown horizontally from the top of a building 21.6 m high. The ball strikes the ground at a point 123 m from the base of the building. Find the x component of its velocity just before it strikes the ground. Find the y component of its velocity just before it strikes the ground.
Compute how long it takes to fall 21.6 m. Call that time T. You should know that formula.
If not, derive it from
H = 123 m = (g/2) T^2.
The vertical velocity when it hits ground is g*T.
The horizontal velocity remains 123 m/T during flight.
To find the x component of the velocity just before the ball strikes the ground, we need to consider the horizontal motion of the ball. Since the ball is thrown horizontally, there is no horizontal acceleration acting on it. Therefore, the x component of its velocity remains constant throughout its motion.
To find the y component of the velocity just before the ball strikes the ground, we need to consider the vertical motion of the ball. The ball is subject to the force of gravity, which causes it to accelerate downwards. We can use the vertical motion equations to solve for the y component of the velocity.
Let's break down the problem step by step:
Step 1: Find the time it takes for the ball to fall from the top of the building to the ground.
Using the formula for free fall motion:
h = (1/2) * g * t^2
where h is the height of the building (21.6 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Plugging in the values:
21.6 = (1/2) * 9.8 * t^2
Simplifying, we get:
t^2 = 4.4
Taking the square root on both sides:
t = 2.1 s
Step 2: Find the x component of the velocity.
Since the ball is thrown horizontally, the x component of its velocity remains constant. We can use the formula:
velocity_x = distance / time
Plugging in the values:
velocity_x = 123 m / 2.1 s
Calculating, we get:
velocity_x ≈ 58.57 m/s
Therefore, the x component of the velocity just before the ball strikes the ground is approximately 58.57 m/s.
Step 3: Find the y component of the velocity.
We can use the equation for vertical motion:
final_velocity_y = initial_velocity_y + (acceleration_y * time)
The initial velocity in the y direction is 0 since the ball is thrown horizontally. The acceleration in the y direction is the acceleration due to gravity (-9.8 m/s^2) and the time is 2.1 s.
Plugging in the values:
final_velocity_y = 0 + (-9.8) * 2.1
Calculating, we get:
final_velocity_y ≈ -20.58 m/s
Therefore, the y component of the velocity just before the ball strikes the ground is approximately -20.58 m/s, indicating that it is moving downward.