A ship RADAR unit uses 315 watts and a radio uses 50 watts. If the equipment is connected to a 50 ampere-hour battery rated at 12.6 volts, how long will the battery last?

To determine how long the battery will last when powering both the ship's RADAR unit and the radio, we first need to calculate the total power consumption of the equipment.

The RADAR uses 315 watts, and the radio uses 50 watts, giving a combined total power consumption of 365 watts (315 + 50).

Next, we need to figure out how much current this total power draw would create at the battery's voltage. The formula used to find the current (in amperes) is:

[ I = \frac{P}{V} ]

Where:

• ( I ) is the current in amperes,

• ( P ) is the total power in watts (365 watts),

• ( V ) is the voltage of the battery (12.6 volts).

Now we can calculate the current:

[ I = \frac{365 \text{ watts}}{12.6 \text{ volts}} ]

This gives a current of approximately 28.89 amperes.

Now that we know the current draw, we can determine how long the battery will last. Since the battery is rated for 50 ampere-hours, this means it can supply 50 amps for 1 hour,