Potential Wifi Product Idea

Hello. I am Wyatt, and i am currently a 14 year old highschool student enrolled in a class called Rising Tycoon. It is a class about entrepneurship and creating a new product, and the product I have thought of is a mobile wifi router that could work on planes and atop the highest of mountains, that could connect to your home router (or any router for that matter) and "charge up" its wifi, which could then be used wherever you are. This product would be a cube that could fit in the palm of your hand and weigh approximately two pounds and cost about 50 dollars, and be waterproof. Would you buy this product if it existed? Why or why not? What other features would you like this product to have? And dont worry about whether or not it is possible to create. Any feedback is helpful. Thanks!