Question

A particle is projected with a velocity of 40m/s at an elevation of 60° to the horizontal. What is the vertical component of the velocity at a height of 50m?

Answer 1

To find the vertical component of the velocity at a height of 50m, we can use the following formula:

Vertical velocity component (Vy) = Initial velocity (V) * sin(theta)

Given: Initial velocity (V) = 40 m/s Elevation angle (theta) = 60 degrees

First, we need to convert the angle from degrees to radians:

theta_rad = theta * (pi/180) theta_rad = 60 * (pi/180) theta_rad = pi/3

Now, we can substitute the values into the formula:

Vy = 40 m/s * sin(pi/3)

Calculating sin(pi/3): sin(pi/3) = sqrt(3)/2

Vy = 40 m/s * (sqrt(3)/2)

Vy = 40 * sqrt(3) / 2

Vy = 20 * sqrt(3) m/s

Therefore, the vertical component of the velocity at a height of 50m is 20 * sqrt(3) m/s.