You're attending a professional basketball game. the home team calls timeout, and, as the music gets cranked up, the t-shirt crew comes out onto the floor to fire team t-shirts into the crowd. like everyone else, you stand up and wave your arms wildly, hoping that one of the t-shirt guys will fire a shirt your way. the t-shirts are fired from a launcher that uses compressed air. one of the launchers is pointed your way, and is just about to launch a t-shirt at a 45° angle from the horizontal. you are a horizontal distance of 20.0 m from the launcher and a vertical distance of 3.00 m above it. neglect air resistance, and assume that the acceleration due to gravity is 9.80 m/s2.

what is the launch speed needed so that the t-shirt reaches you, rather than one of the hordes of people sitting near you?

The launch speed has to be 15.2 m/s so that the T-shirt reaches you.

Explanation:

The equation for the position of an object moving in a parabolic motion is as follows:

r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)

Where:

r = vector position at time t

x0 = initial horizontal position

v0 = initial velocity

t = time

α = launching angle

y0 = initial vertical position

g = acceleration due to gravity

Please, see the figure for a description of the problem. The vector "r" is the position vector the t-shirt must have to reach you.

As you can see from the figure, the x-component of the vector "r" is 20.0 m and the y-component is 3.00 m. Then, using the equations for the vector "r" we can obtain the time of flight and the initial velocity:

x = x0 + v0 · t · cos α    (since the origin of the frame of reference is located at the launching point, x0 = 0)

x = v0 · t · cos α

Solving for v0:

x/(t · cos α) = v0

20.0 m/ t · cos 45° = v0

Replacing v0 in the equation for the y-component of the vector "r":

y =  y0 + v0 · t · sin α + 1/2 · g · t²       (y0 = 0, same as x0)

y = 20.0 m · sin 45°/cos 45° - 1/2 · 9.80 m/s² · t²

3.00 m = 20. 0 m · tan 45° -  1/2 · 9.80 m/s² · t²

3.00 m - 20. 0 m · tan 45° = -4.90 m/s² · t²

-17.0 m/  -4.90 m/s² = t²

t = 1.86 s

Now, with the time, we can calculate v0:

v0 = 20.0 m/ t · cos 45° = 20.0 m/ 1.86 s · cos 45° = 15.2 m/s

The launch speed has to be 15.2 m/s.

with the invention of the automobile, the woman of the house could drive to the store and get groceries. women were also free to socialize more. during world war ii women were allowed to work in factories to the war effort and could drive to work or ride mass transit buses to their jobs.

15.3 cos 65 degrees trig