Question

An inclined plane of inclination (&) has a length of 15m .If a body rolls down the plane freely along the entire length with an acceleration 5ms^-2 , calculate the

(a)angle (&)
(b)height of the plane
Take g=10m/s²

Answer 1

To calculate the angle of incline (&), we use the formula a = g sin(&), which gives us an angle of 30 degrees. The height of the inclined plane is then found using trigonometry, resulting in a height of 7.5 m.

Step-by-step explanation:

Calculating the Incline Angle and Height

For a body rolling down an inclined plane freely, the acceleration a along the incline is given by the component of gravitational acceleration g along the plane. This relation is expressed as a = g sin(&), where (&) is the angle of inclination. We know from the problem that a = 5 m/s^2 and g = 10 m/s^2. We can solve for angle (&) using the equation:

sin(&) = a/g => sin(&) = 5/10 => sin(&) = 0.5.

So, the angle of inclination (&) can be calculated using the inverse sine function:

(&) = sin^{-1}(0.5)

Which gives us (&) = 30 degrees.

Next, we can calculate the height of the inclined plane using trigonometry. Since the length of the incline is 15 m, we use:

height = length × sin(&) => height = 15 m × sin(30 degrees) => height = 15 m × 0.5.

Therefore, the height of the plane is 7.5 m.