Agolfer tees off and hits a golf ball at a speed of 31 m/s and at an angle of 35 degrees. what is the maximum height attained by the ball? round the answer to the nearest meter.

Let's write the law of motions of the ball on both x and y axis. The motion of the ball is a uniform motion on the x-axis, with constant velocity, and uniformly accelerated motion on the y-axis, with constant acceleration g:


where  is the initial speed of the ball and  is the angle at which the ball is launched.

The ball reaches its maximum height when its vertical velocity is zero. The law for the vertical velocity is:

By requiring , we find the time t at which the ball reaches the maximum height:



And if we substitute this time t inside the law of motion on the y-axis, y(t), we find the maximum height of the ball:

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