Answer to Question #103155 in Mechanics | Relativity for Katie Jennings

Question

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?

Answer 1

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