You break it down into horizontal and vertical components. In this situation, the vertical component is sin 35 * 1000 and the horizontal component is cos 35 * 1000. The initial vertical velocity is 572.9 m/s, and the initial horizontal velocity is 819.6 m/s.
The key to solving this problem is finding time. So you need to break it down into two sections: as the object rises, and as the object falls. For the first part, you take the initial vertical velocity, 572.9 m/s and divide it by gravity, 9.8 m/s^2, to get the time to the maximum height, which is 58.5 seconds.
The next step is to find the maximum height. To do this, you can simply find the average velocity and multiply it by the time, which we already have. The average velocity is simply the initial vertical velocity divided by the final vertical velocity (0 m/s): 286.5 m/s. Multiply that by the time, and get 16760 m.
Finally, you need to determine the time it takes to fall and hit the water. Finding the distance the object falls is simple, just take the 16760 m (maximum height) and add 60 m (height of the cliff), to get 16820 m. Just plug that into the equation for a free-falling body to find the time, 58.6 sec.
Add the two times together, 58.5 sec + 58.6 sec = 117.1 sec, which is the amount of time the object is in the air. Now go back to the beginning, and use the initial horizontal velocity times the time to get the answer: 95975 m.