Question

A projectile is launched from point O atan angle of 22° with an initial velocity of15 m/s up an incline plane that makes anangle of 10° with the horizontal. Theprojectile hits the incline plane at a pointM. Find the distance from point o topoint M.​

Answer 1

The distance from point O to point M, where the projectile hits the incline plane, is approximately 27.8 meters.

Step-by-step explanation:

To find the distance from point O to point M, we can use the kinematic equations of motion. The horizontal and vertical motions can be treated independently.

Firstly, calculate the time of flight (t) using the vertical motion. The equation for the vertical displacement (h) is given by:

`\[ h = (1)/(2) g t^2 \]`

where (g) is the acceleration due to gravity. Solving for (t), we get:

`\[ t = \sqrt{(2h)/(g)} \]`

Substitute the given values (h) is the vertical component of the incline plane, which is
`\(15 \sin(10°)\)) and \(g \approx 9.8 \, \text{m/s}^2\).`

Once you have (t), find the horizontal distance using the equation:

`\[ \text{Horizontal Distance} = \text{Horizontal Velocity} * t \]`

The horizontal velocity
`(\(v_x\)) is given by \(15 \cos(22°)\).` Substitute the values and calculate the horizontal distance.

The total distance from point O to point M is the horizontal distance traveled by the projectile.