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?
time to fall to ground:
hf=hi+1/2 g t^2
t=sqrt(2*2.8/9.8)
speed : distance/time=12.75ft/t
convert that to mph (88ft/sec=60miles/hr)
speed hit ground: horizontal componetn 12.75, vertical component=32ft/s^2* timefalling
To calculate the player's break shot speed in mph, we need to convert the distance traveled by the ball into time first.
To convert the distance from feet to miles, we divide the distance by 5280 (since there are 5280 feet in a mile):
Distance in miles = Distance in feet / 5280
In this case, the distance traveled by the ball is 12.75 ft. Therefore,
Distance in miles = 12.75 / 5280
Next, we need to convert the time taken into hours.
Since the player's break shot was measured at 32 mph, we can use this speed to calculate the time it took for the ball to cover the given distance:
Time in hours = Distance in miles / Speed in mph
In this case, the distance in miles is 12.75 / 5280, and the speed is 32 mph.
Time in hours = (12.75 / 5280) / 32
Finally, to calculate the break shot speed in mph, we divide the distance traveled (in feet) by the time taken (in hours):
Break shot speed in mph = Distance in feet / Time in hours
In this case, the distance traveled is 12.75 ft, and the time taken is ((12.75 / 5280) / 32).
Break shot speed in mph = 12.75 / ((12.75 / 5280) / 32)
To calculate the speed at which the ball hit the ground, we need to calculate the time it took for the ball to hit the ground. Since we have the height from the floor (2.80 ft), we can use the equation of motion:
s = ut + (1/2)gt^2
Where:
- s is the height from the floor
- u is the initial velocity of the ball vertically upwards
- t is the time taken
- g is the acceleration due to gravity (approximately -32.2 ft/s^2)
Since the ball starts from rest vertically upwards, the initial velocity (u) is 0 ft/s.
s = (1/2)gt^2
We solve this equation for t to find the time it took for the ball to hit the ground.
Once we have the time (t), we can calculate the speed at which the pool ball hit the ground:
Speed at which the ball hit the ground = g * t
In this case, g is approximately -32.2 ft/s^2, and t is the time calculated from solving the equation.
Speed at which the ball hit the ground = -32.2 * t
Now you have the formulas to calculate the break shot speed in mph and the speed at which the ball hit the ground. Plug in the values and calculate the answers.