How Fast Does a Bowling Ball Travel When It Falls Off a Table?

[Michael17]

Bowling ball and table!

Can anyone please help me figure this one out;

A bowling ball of mass 7.5kg traveling at 10m/s rolls off a horizontal table 1.0 m high. Calculate the velocity of the ball as it reaches the floor, ignoring air resistance and having an acceleration due to gravity of 9.8m/s.

 

[LowlyPion]

Can anyone please help me figure this one out;

A bowling ball of mass 7.5kg traveling at 10m/s rolls off a horizontal table 1.0 m high. Calculate the velocity of the ball as it reaches the floor, ignoring air resistance and having an acceleration due to gravity of 9.8m/s.

They gave you the horizontal component of velocity. They want you to find the vertical component and then combine the 2 like Pythagoras would to yield the answer for the magnitude of the |velocity| vector. Now they may also want you to give the direction. (That would be tan^-1 of the ratio of the 2.)

 

[thomate1]

I would approach this problem by using the principles of Newton's laws of motion and the equations of motion to solve for the velocity of the bowling ball as it reaches the floor.

Firstly, we need to identify the known values in this problem. We know the mass of the bowling ball (7.5kg), its initial velocity (10m/s), the height of the table (1.0m), and the acceleration due to gravity (9.8m/s). Our goal is to find the final velocity of the ball as it reaches the floor.

Using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we can rearrange it to solve for v: v = √(u^2 + 2as).

Substituting the known values, we get v = √(10^2 + 2(9.8)(-1)). This gives us a final velocity of approximately 7.07m/s as the ball reaches the floor.

In conclusion, the velocity of the bowling ball as it reaches the floor is approximately 7.07m/s. This calculation is based on the assumption that there is no air resistance and the acceleration due to gravity is 9.8m/s. It is important to note that in real-life scenarios, there may be other factors that could affect the final velocity of the ball, such as air resistance or the surface of the table.