Answer :
Final answer:
The height at which the ball hits the wall is calculated using the equations of projectile motion, and it is approximately 11.1 meters.
Explanation:
The problem you're asking about involves understanding of projectile motion. The idea behind this concept is that the motion of an object, like the ball in the problem, can be described in terms of its horizontal and vertical motion.
To find the height at which the ball hits the wall, we first need to know how much time it takes for the ball to travel the horizontal distance to the wall. We can calculate this by using the equation t = d / v where d is the distance (40 m) and v is the horizontal component of velocity. In this case, the horizontal velocity (Vx) is given by Vx = V * cos(theta) = 24 m/s * cos(36.9) which gives us Vx = 19.187 m/s This determines our time as t = d / v = 40 m / 19.187 m/s = 2.08 s.
Now, we can calculate the vertical height (h) at this time. We use the equation h = (Vy * t) - 0.5 * g * t^2. Vy is the initial vertical velocity, calculated similarly to Vx but using sine instead of cosine: Vy = V * sin(theta) = 24 m/s * sin(36.9) = 14.08 m/s. In this formula, g is the gravitational acceleration (9.8 m2/s) and t is our previously calculated time. Plug in our values h = (14.08 m/s * 2.08 s) - 0.5 * 9.8 m^2/s * (2.08 s)^2, simplified the height at which the ball hits the wall is approximately 11.1 meters.
Learn more about Projectile Motion here:
https://brainly.com/question/29545516
#SPJ11