ap physics 1 problem

Question

'Serah the Terrah' fires a slingshot at a 63.5-degree angle from the horizontal with a speed of 18.5 m/s. If the marble hits a window of Josie's room, 6.80 meters above the slingshot on its way down, find the horizontal distance the marble travels when it breaks the window.

Answer 1

First we need to find the time it takes to reach the window. This can be found from the equation

H = V x sin (63.5) x t - 1/2 g t² where H = window height, V = 18.5 m/s, g acceleration of gravity, t = time.

V x sin (63.5) is the vertical component of the velocity. Everything is given except the time. Solving for the time results in a quadratic equation that can be solved using the quadratic formula to give two results. The bigger result would be the time when the marble strikes the window on its way down.

Once you have the time, you can use D = 18.5 x cos(63.5) x t to calculate the distance D to the window.

If I didn't make any computational error, the time is 2.89 s, and the distance 23.9 m