Yes, whales can jump and even perform a number of areal stunts.
In fact some species of whale are very acrobatic and can perform many different amazing feats including jumping, flipping breaching and bow riding.
Jumping however is more common among the smaller toothed whale species as their smaller size and lighter body makes it easier for them to leap out of the water.
Breaching occurs when a whale lifts at least 40% of its body out of the water.
Some baleen whale are able to expose as much as 90% of their bodies above the surface before they reestablish contact with the water.
Surprisingly these breaches only take up a small amount of the whales energy (less than 0.100%) but a large amount of breaches over a short period of time can eventually tire the whale out.
It is also important to note that not all species of whale are known for such acrobatic maneuvers.
Some whales prefer to live a very inactive, sedentary and docile lifestyle, and are more likely to shy away from people or log around the ocean’s surface than to perform breaches, spy-hops, jumps and lunges.
Dolphins are also part of the toothed whale family and are well-known for their ability to jump and flip out of the water.
And some dolphins are capable of jumping more than 25 ft. into the air!
Because of their small size they are ideal for performing acrobatic feats at marine parks and live aquatic shows.
Porpoise also fit into the toothed whale suborder, however they tend to be less acrobatic than some of the dolphin species.
Unfortunately whales are way too large for aquariums so the closest people will get to seeing whales jump is to look for hosted whale watching tours.
In terms of communication jumping is one of the many ways that whales communicate with each other.
Jumping can be used as a form of play, to maintain a good awareness of their environment and to show their youthfulness and health when trying to attract a mating partner among other things.
Whales are also known to spy-hop, charge at one another, vocalize through songs, moans, clicks and whistles and lob-tail among in order to communicate their intentions to other whales.
When combining these physical gestures with vocal communication whales have developed a very effective and sophisticated system for communicating with one another.