A 72 g baseball rolls off a 1.5 m high table and strikes the floor a distance of .8 m away from table. How fast is it rolling on the table before it fell off?? Accel of gravity is 9.81 m/s2.
I will be happy to critique your thinking on this. You know how much time it took the ball to fall 1.5m.
Figure out how long it takes an object to fall 1.5 meters starting from zero vertical speed component at 9.81 m/s^2.
That is how long it is in the air.
Then how fast was its horizontal velocity component to go .8 meters in that time that you found?
The only thing that is not relevant is the mass of the ball.
To calculate the speed at which the baseball is rolling on the table before falling off, we can use the principle of conservation of energy.
The potential energy the baseball has while on the table is converted into kinetic energy when it falls off the table. The formula for potential energy is given by:
Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
In this case, the mass (m) of the baseball is given as 72 g (which is equivalent to 0.072 kg), the acceleration due to gravity (g) is 9.81 m/s^2, and the height (h) of the table is 1.5 m. So, the potential energy of the baseball while on the table is:
PE = 0.072 kg × 9.81 m/s^2 × 1.5 m
Next, we can calculate the kinetic energy of the baseball when it hits the floor using the formula:
Kinetic Energy (KE) = 1/2 × mass (m) × velocity^2
Here, we know the distance (d) the baseball traveled before hitting the floor, which is given as 0.8 m. Since the baseball rolls without slipping, the distance it travels is equal to the circumference of the ball, which is given by 2πr, where r is the radius of the ball. We don't know the radius, but we can solve for it.
Circumference (C) = 2πr = distance traveled (d)
Substituting the given value of d, we have:
2πr = 0.8 m
Solving for r:
r = 0.8 m / (2π) = 0.127 m (approximately)
Now that we know the radius of the ball, we can calculate the circumference and use it to find the velocity (v) of the ball when it hits the ground:
Circumference (C) = 2πr = 2π × 0.127 m
The distance traveled equals the circumference, so we have:
C = 2π × 0.127 m = 0.8 m
Since the linear distance (d) is equal to the circumference, we can use this to find the velocity (v):
v = d / time taken (t)
We need to calculate the time it took for the ball to fall this distance. We can find this time using the equation of motion for a falling object:
d = (1/2) × acceleration due to gravity (g) × time^2
Substituting the given values:
0.8 m = (1/2) × 9.81 m/s^2 × time^2
Simplifying and solving for time:
time^2 = (2 × 0.8 m) / 9.81 m/s^2
time^2 ≈ 0.1627
time ≈ √(0.1627) = 0.403 s (approximately)
Now, we can substitute the values of distance (d) and time (t) into the equation to find the velocity (v):
v = 0.8 m / 0.403 s
v ≈ 1.98 m/s (approximately)
Therefore, the baseball was rolling on the table with a speed of approximately 1.98 m/s before it fell off.