Question

The cable at B is pulled downwards at 4 ft, and the speed is decreasing at 2 ft/second. What is the velocity and acceleration of block A at this instant?

Answer 1

To determine the velocity and acceleration of block A at the given instant, we need to consider the relationship between the motion of block A and the movement of the cable at B.

Let's assume that block A is connected to block B by an inextensible cable. When block B is pulled downwards at a speed of 2 ft/second, this implies that block A is also moving downwards, driven by the cable.

Given: Displacement of block B ($s_B$) = -4 ft (negative because it is moving downwards) Speed of block B ($v_B$) = -2 ft/second (negative because it is decreasing)

To find the velocity and acceleration of block A, we need to determine their relationship using the constraint imposed by the inextensible cable.

Since the cable connecting the blocks is inextensible, the displacement of block A ($s_A$) will be the same as that of block B ($s_B$).

$s_A=s_B=-4$ ft

The velocity of block A ($v_A$) can be found by taking the derivative of the displacement with respect to time:

vA=dsAdt=dsBdtv_A = frac{{ds_A}}{{dt}} = frac{{ds_B}}{{dt}}vA​=dtdsA​​=<span style="top: -2.655e