Question

An object is thrown horizontally from a tower h meters high with velocity of square root of 2gh m/ s. its velocity on striking the ground will be square root of xgh. find x

Answer 1

Often, I do my best to emphasize that basic Physics consists of just a few important principles and ideas that, if one uses in an intelligent way with Mathematics, can be used to derive everything else. Thus, I will solve this question based only on a few basic ideas from Kinematics. First, we write down the acceleration in each direction;



Now, let us solve the first equation for the vertical velocity as a function of time. Based on the information in the question, we know that the initial vertical velocity has to be 0 at t=0. Therefore;











Now, we have another differential equation that we must solve. Now, in this case, we have to be careful about where we define our 0. It’s not so much that it will affect the final equation. It’s just that some origins are easier to handle than others. I’m going to assume that the origin is at the foot of the tower. In other words, the position of the stone at t=0 is h. Therefore;









Now, we are very interested in the time that it takes for the stone to be at the position when y=0. Physically, that just means that the stone is on the ground. Now, we want the time when the stone hits the ground. That’s pretty easy to do;







Rather easy algebra. Now, we’ve completely figured out what we needed to from the vertical part of the motion. Let’s do the horizontal part now. The differential equation that we are trying to solve is given as follows;



Answer 2

Answer:

Liquid water has one of the highest specific heats among common substances, about 4182 J/(K kg) at 20 °C; but that of ice just below 0 °C is only 2093 J/(K kg).