Question

A small smooth object slides from rest down a smooth plane inclined at 30° to the horizontal. What is the time to reach the bottom if the plane is 5 m long (g = 10 m/s²)?

a) 1 second
b) 1.5 seconds
c) 2 seconds
d) 2.5 seconds

Answer 1

The time it takes for the small smooth object to reach the bottom of the inclined plane is 1 second.

Step-by-step explanation:

To find the time it takes for the small smooth object to reach the bottom of the inclined plane, we can use the equations of motion. Since the object is sliding down a smooth plane, friction can be ignored. We can use the equations of motion in the vertical direction to solve for the time.

First, we need to find the vertical component of the object's velocity at the bottom of the incline. We can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the object starts from rest, so the initial velocity u is 0 m/s. The acceleration a is equal to the acceleration due to gravity, which is 10 m/s². We can plug in these values to find the final velocity v.

v = u + at
v = 0 + 10 * t
Now, we need to find the time it takes for the object to travel down the incline. We can use the formula s = ut + (1/2)at², where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration. In this case, the distance traveled down the incline is equal to the length of the incline, which is 5 m.

s = ut + (1/2)at²
5 = 0 * t + (1/2) * 10 * t²
5 = 5t²
t² = 1
t = 1 s

Therefore, the time it takes for the small smooth object to reach the bottom of the inclined plane is 1 second.