The top of the pool table is 2.80 ft from the floor. The placement of the tape is such that 0 feet aligns to the edge of the table (as shown). The winner of the competition wants to know if he has broken the world record for the break shot of 32 mph. His ball landed a distance 12.75 ft from the table edge. Calculate his break shot speed in mph and At what speed did his pool ball hit the ground?
h = 0.5g*t^2.
2.80 = 16t^2
t = 0.424s = Fall time.
a. d = Xo*t.
12.75 = Xo*0.424.
Xo = 30.1 ft/s = Initial hor. velocity of the ball.
Xo = 30.1ft/s * 1mi/5280ft * 3600s/h =
20.52 mi/h.
b. Y^2 = Yo^2 + 2g*h.
Y^2 = 0 + 64*2.80 = 179.2
Y = 13.40 ft./s. = Ver. component of final velocity.
V = sqrt(Xo^2+Y^2).
Xo = 30.1ft/s, Y = 13.40ft/s.
To calculate the break shot speed in mph and the speed at which the pool ball hit the ground, we need to follow a few steps:
Step 1: Convert the given measurements to a consistent unit.
Since we are looking to calculate speeds, we will convert all measurements to feet.
The height of the pool table is given as 2.80 ft.
The distance from the table edge to where the ball landed is given as 12.75 ft.
Step 2: Calculate the time of flight for the ball.
To calculate the time of flight, we'll use the formula for vertical motion:
d = v0t + (1/2)gt^2,
where d is the vertical distance traveled, v0 is the initial vertical velocity, g is the acceleration due to gravity (32.2 ft/s^2), and t is the time of flight.
In this case, the vertical distance traveled is the height of the table, which is 2.80 ft.
2.80 = v0t - (1/2)(32.2)t^2.
Simplifying the equation, we get:
(1/2)(32.2)t^2 - v0t + 2.80 = 0.
Next, we'll solve this quadratic equation to find the value of t.
Step 3: Calculate the initial vertical velocity.
To calculate the initial vertical velocity, we'll use the formula:
v0 = gt,
where g is the acceleration due to gravity and t is the time of flight. We already have the value of t from the previous step.
Step 4: Calculate the horizontal distance traveled by the ball.
To calculate the horizontal distance traveled by the ball, we'll use the formula:
d = v0x * t,
where d is the horizontal distance, v0x is the initial horizontal velocity, and t is the time of flight.
In this case, the horizontal distance traveled is the distance from the table edge to where the ball landed, which is 12.75 ft.
Step 5: Calculate the break shot speed in mph.
The break shot speed is the initial velocity of the ball. We can calculate it using the horizontal distance traveled and the time of flight.
To convert it to mph, we'll multiply the velocity by the appropriate conversion factor.
Step 6: Calculate the speed at which the ball hit the ground.
The speed at which the ball hits the ground is the vertical velocity at the point of impact. We can calculate it using the initial vertical velocity and the acceleration due to gravity.
To convert it to mph, we'll multiply the velocity by the appropriate conversion factor.
By following these steps, we can accurately calculate the break shot speed in mph and the speed at which the ball hit the ground.