Aball is tossed from an upper-story window of a building. the ball is given an initial velocity of 7.90 m/s at an angle of 18.0° below the horizontal. it strikes the ground 4.00 s later. (a) how far horizontally from the base of the building does the ball strike the ground? 30.04 correct: your answer is correct. m (b) find the height from which the ball was thrown. incorrect: your answer is incorrect. work only with the vertical components of these quantities. this part of the problem is then a 1-dimensional free-fall example. m (c) how long does it take the ball to reach a point 10.0 m below the level of launching? s

In order to solve the problem, let's write the equations of motion first. Let's take the x-axis as the horizontal direction, and the y-axis on the vertical direction (pointing downward). Calling  the initial velocity, and  the angle below the horizontal, the equations of motion are

 
where  is the gravitational acceleration.

(a) To find the distance covered by the ball horizontally, we must simply calculate Sx at the time the ball hits the ground (t=4.0 s):


(b) The height from which the ball was thrown is the value of Sy at 4.0s, which is the distance covered by the ball before hitting the ground:


(c) To calculate how long does it take to the ball to reach 10.0 m below the initial point, we have to find the time at which Sy(t)=10.0 m. This means we must solve the following equation:

Using the data of the problem, we can solve this equation. We find two solutions for t: one is negative, so we can neglect it. The second one, which is the solution of the problem, is t=1.19 s.

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