Answer to Question #269791 in Physics for Fanah

Question

Children playing in a playground on the flat roof of a city school lose their ball to the parking lot.One of the teachers kicks the ball back up to the children.The playground is 5.70m above the parking lot,and the school building's vertical wall is h=6.80m high, forming a 1.10m high railing around the playground.The ball is launched at an angle of 53.0° above the horizontal at a point d=24.0m from the base of the building wall.The ball takes 2.20s to reach a point vertically above the wall.

(a).Find the speed (in m/s) at which the ball was launched .

(b).Find the vertical distance (in m)by which the ball clears the wall.

(c).Find the horizontal distance (in m)from the wall to the point on the roof where the ball lands.

Answer 1

a)

$$24=v_i\cos{53}(2.2)\\v_i=18.1\frac{m}{s}$$

b)

$$y=18.1\sin{53}(2.2)-0.5(9.8)(2.2)^2-6.8\\=1.29\ m$$

c)

$$5.7=x\tan{53}-\frac{9.8}{2(18.1\cos{53})^2}x^2\\x=27\ m\\\Delta x=27-24=3\ m$$