Johnny loves the weather and wants to be a meteorologist someday. He is failing his calculus class and tells his mom she does not understand why he...

A meteorologist is an individual that scientifically studies the atmosphere. Part of a meteorologist job is being an operational forecaster. An operational forecaster analyses weather conditions and issues forecasts, warnings and alerts to inform the public about severe weather conditions in an area.

Now this where calculus is important as an operational forecaster: 

In order to be an excellent operational forecaster one needs to be able to predict weather accurately. In order to predict weather correctly one has to develop excellent numerical weather models. These numerical weather models require a good understanding of calculus so that an operational forecaster an a deep understanding of atmospheric processes. These numerical models include variables such as temperature, humidity, pressure, etc. and can be solved using calculus thus enabling us to forecast weather accurately up to 7 days. 

Additionally, meteorology is a specialized mathematical field. An individual that does not take calculus during his academics will not likely succeed in the field and might be without a job.