At a football game, an air gun fires T-shirts into the crowd. The gun is fired at an angle of 32° from the horizontal with an initial speed of 30 m/s. A fan who is sitting 60 m horizontally from the gun, but high in the stands, catches a T-shirt. A) How long does it take for the T-shirt to reach the fan?
B) At what height h is the fan from the ground?

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andresdbv andresdbv · Answer 1 · 2019-09-17T01:39:42+02:00

Answer:

A) The time it takes for the T-shirt to reach the fan is 2.3582s

B) The height the fan is from the ground is 10.2438m

Explanation:

First, we need to find the velocity vectors for each axe:

[tex]v_{x}=30*cos(32\textdegree)=25.44\frac{m}{s}\\ v_{x}=30*sin(32\textdegree)=15.90\frac{m}{s}[/tex]

Next, using the movement equation for the x axis, we get the time:

[tex]D=v_{x}*t\\t=\frac{D}{v_{x}}=2.3585s[/tex]

Finally, using the movement equation for the y axis, we find the height (assuming the gravity as 9,8[tex]\frac{m}{s^{2}}[/tex])

[tex]h=v_{y}*t-\frac{g*t^{2}}{2}=10.2438\frac{m}{s^{2}}[/tex]