A ball bearing is placed on an inclined plane and begins to roll.The angle of elevation of the plane is radians.The distance (in meters)the ball bearing rolls in t seconds is .Determine the speed of the ball bearing after t seconds.Round to one decimal place.
A)speed: meters per second
B)speed: meters per second
C)speed: meters per second
D)speed: meters per second
E)speed: meters per second

Question

A ball bearing is placed on an inclined plane and begins to roll.The angle of elevation of the plane is  radians.The distance (in meters)the ball bearing rolls in t seconds is  .Determine the speed of the ball bearing after t seconds.Round to one decimal place. ​
A)speed: meters per second 
B)speed: meters per second 
C)speed: meters per second 
D)speed: meters per second 
E)speed: meters per second

Quizplus · Accepted Answer

The speed of the ball bearing can be found using the formula:
speed = distance/time
We are given the distance the ball bearing rolls in t seconds as well as the angle of elevation of the plane. However, we do not have the time it takes for the ball bearing to roll that distance. Therefore, we need to find an equation that relates the distance, time, and angle of elevation.
One such equation is:
distance = (1/2) * acceleration * t^2 * cos(theta)
where acceleration is the acceleration due to gravity (9.81 m/s^2) and theta is the angle of elevation in radians.
Rearranging this equation, we get:
t = sqrt((2*distance)/(acceleration*cos(theta)))
Substituting the given values, we get:
t = sqrt((2*11)/(9.81*cos(11)))
t = 1.320 seconds (rounded to 3 decimal places)
Now that we know the time it takes for the ball bearing to roll the distance, we can find its speed:
speed = distance/time
speed = 11/1.320
speed = 8.333 meters per second
Rounded to one decimal place, the answer is:
C) speed: 8.3 meters per second

A Ball Bearing Is Placed on an Inclined Plane and Begins