A playground is on the flat roof of a city school, 5.1 m above the street below (see figure). The vertical wall of the building is h = 6.50 m high, forming a 1.4-m-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of θ = 53.0°; above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall.
(a) Find the speed at which the ball was launched.
There are actually 3 parts to this problem. Currently I only need help with part (a) because I need that to answer the other 2 parts, but I may need help with other parts as well.
The program I am using to submit my work says my answer differs within 10% of the correct value but I have rechecked my answer several times and found no mistakes and I didn't round off until the final answer. What am I doing wrong?
Here are the calculations I have carried out to find the initial velocity:
I used the equation
where , the acceleration vector due to gravity; is the is the y component of the initial velocity vector; is the y coordinate (the height) of the initial position of the ball; is time; and is the y coordinate of the final position of the ball.
Since it takes the ball takes 2.20 s to reach a point vertically above the wall, I substituted and , the height of the wall, into the above equation. would of course be 0m since the ball starts at ground level.
Note: I did not actually round off here for my next calculation.
I keep getting this same answer. What am I doing wrong?