An autographed baseball rolls off a 0.5m high desk and strikes the floor 0.4m away . How fast was the ball traveling when it hit ?
To determine the speed at which the autographed baseball was traveling when it hit the floor, we can use a physics formula known as the kinematic equation. The equation we will use is the equation of motion for an object in free fall:
v^2 = u^2 + 2as
Where:
v = final velocity (which is what we want to find)
u = initial velocity (the speed at which the ball was rolling off the desk, which is what we want to find)
a = acceleration due to gravity (which is approximately 9.8 m/s^2, acting vertically downwards)
s = distance traveled (0.4m horizontally in this case)
Now let's solve the equation step by step:
1. Since the ball was rolling off the desk horizontally, there is no initial vertical velocity (u_y = 0). Therefore, the initial velocity is only in the horizontal direction: u = u_x.
2. The vertical distance traveled (s_y) is 0.5m, so we can calculate the time it takes for the ball to fall using the formula for vertical distance under constant acceleration:
s_y = (1/2)gt^2
Where:
s_y = vertical distance traveled
g = acceleration due to gravity
t = time
0.5 = (1/2) * 9.8 * t^2
1 = 9.8 * t^2
t^2 = 1 / 9.8
t = sqrt(1 / 9.8)
3. Now that we know the time it takes for the ball to fall, we can find the horizontal velocity (u_x) using the formula for horizontal distance under constant velocity:
s_x = u_x * t
Where:
s_x = horizontal distance traveled
u_x = horizontal velocity
t = time
0.4 = u_x * sqrt(1 / 9.8)
0.4 * sqrt(9.8) = u_x
u_x = 0.4 * sqrt(9.8)
4. Finally, we can calculate the speed (v) at which the ball was traveling when it hit the floor using the equation:
v^2 = u^2 + 2as
Since the ball only moves horizontally, there is no vertical acceleration or displacement, so the equation simplifies to:
v^2 = u_x^2
v = u_x
Therefore, the speed at which the ball was traveling when it hit the floor is approximately 0.4 * sqrt(9.8) m/s.
V^2 = Vo^2 + 2g*h
Vo = 0
g = 9.8
h = 0.5 m.
Solve for V.