Question #103155

You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 33° from the edge of the building with an initial velocity of 21 m/s and lands 65 meters away from the wall. How tall, in meters, is the building that the child is standing on?

Expert's answer

Answer:-

Resolve the initial velocity X-component

"V_{x}=V_{0}cos\\theta=21\\times cos33\\degree=17.62 \\frac m s"

Resolve the initial velocity Y-component

"V_{y}=V_{0}sin\\theta=21\\times sin33\\degree=11.44 \\frac m s"

Time taken to travel 65 m along X-axis is.

"\\to s=v_{x}t\\\\\\rightarrow t=\\frac{s}{v_{x}}=\\frac{65}{17.62}\\ =3.68 sec"

Total flight time of the ball is 3.68 sec

Now,

Find the height of building as follows.

"S_{y}-S_{_{yo}}=V_{y}t-\\frac{1}{2}gt^{2}\\\\"

Here,

"\\because" S_{y}=0 (final height)

V_{y}= 11.44 m/s (Initial velocity)

Find

S_{yo}= ? (Initial height)

"0-S_{yo}=v_{y}t-\\frac{1}{2}gt^{2}\\\\"

Now,

"S_{yo}=\\left ( \\frac{1}{2}\\times 9.81\\times (3.68)^{2} \\right )-\\left ( 11.44\\times 3.68 \\right )\\\\"

"S_{yo}=24.32m"

So,

Answer:-

The child is on a roof that is 24.32 m tall

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