Answer :
The speed at which the ball rises is 2.24 m/s.
What is power output?
Power output refers to the amount of power that a device, machine, or system produces or generates. It is a measure of the rate at which work is done or energy is transferred, and is usually expressed in units of watts (W) or kilowatts (kW).
We can use the formula for power to find the speed at which the ball rises. The power output of the motor is given by:
Power = Work done / time taken
Since the ball is lifted at a constant speed, the work done by the motor is equal to the gravitational potential energy gained by the ball, which is given by:
Work done = mgh
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s²), and h is the height through which the ball is lifted. The time taken to lift the ball is equal to the height of the lift divided by the speed of the lift, which is given by:
time taken = h / v
where v is the speed of the lift. Substituting these expressions into the formula for power, we get:
Power = mgh / (h/v)
Power = mgv
Solving for v, we get:
v = Power / (mg)
v = 159 W / (7 kg x 9.8 m/s²)
v = 2.24 m/s
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