Question

At a given instant, the crane is moving along the track with a velocity vCD =10 m/s and acceleration of 5 m/s2. Simultaneously, it has the angular motions shown. If the trolley T is moving outwards along the boom AB with a relative speed of 8 m/s and relative acceleration of 4 m/s2, determine the velocity and acceleration of the trolley with respect to a fixed frame.

Answer 1

9 m/s^2.

Step-by-step explanation:

To solve this problem, we can use relative velocity and acceleration equations.

First, let's find the velocity and acceleration of point D with respect to a fixed frame:

vD = vC + vCD = 10 m/s

aD = aC + aCD = 5 m/s^2

Next, let's find the velocity and acceleration of point T with respect to point D:

vTD = 8 m/s

aTD = 4 m/s^2

Finally, we can find the velocity and acceleration of point T with respect to a fixed frame:

vT = vD + vTD = 10 + 8 = 18 m/s

aT = aD + aTD = 5 + 4 = 9 m/s^2

Therefore, the velocity of the trolley with respect to a fixed frame is 18 m/s and the acceleration of the trolley with respect to a fixed frame is 9 m/s^2.