Afarmer lifts his hay bales into the top loft of his barn by walking his horse forward with a constant velocity of 1 ft/s. determine the velocity and acceleration of the hay bale when the horse is 10 ft away from

The velocity of the hay bale is - 0.5 ft/s and the acceleration is

Solution:

As per the question:

Constant velocity of the horse in the horizontal,

Distance of the horse on the horizontal axis, x = 10 ft

Vertical distance, y = 20 ft

Now,

Apply Pythagoras theorem to find the length:

Now,

                           (1)

Differentiating equation (1) w.r.t 't':

where

= Rate of change of displacement along the horizontal

= Rate of change of displacement along the vertical

= velocity along the x-axis.

= velocity along the y-axis

Acceleration of the hay bale is given by the kinematic equation: