Question

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?

Answer 1

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

Step-by-step explanation:

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

`v_(x)=30*cos(32\textdegree)=25.44(m)/(s)\\ v_(x)=30*sin(32\textdegree)=15.90(m)/(s)`

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

`D=v_(x)*t\\t=(D)/(v_(x))=2.3585s`

Finally, using the movement equation for the y axis, we find the height (assuming the gravity as 9,8
`(m)/(s^(2))`)

`h=v_(y)*t-(g*t^(2))/(2)=10.2438(m)/(s^(2))`