Question

At a football game, an air gun fires t-shirts into the crowd. The gun is fired at an angle of 34° from the horizontal with an initial speed of 26 m/s. A fan who is sitting 60 m horizontally from the gun, but high in the stands, catches a t-shirt. What is the vertical distance between the fan and the gun when the t-shirt is caught?

Answer 1

To find the vertical distance between the fan and the gun when the t-shirt is caught, we can calculate the time it takes for the shirt to reach the fan and then use that time to find the vertical distance using the appropriate formulas.

Step-by-step explanation:

To find the vertical distance between the fan and the gun when the t-shirt is caught, we can break down the initial velocity into its horizontal and vertical components. The initial speed of 26 m/s can be split into a horizontal component (26*cos(34°)) and a vertical component (26*sin(34°)).

Since the horizontal distance between the fan and the gun is 60 m, and the horizontal component of the velocity is constant, we can calculate the time it takes for the shirt to reach the fan using the formula t = d/v:

t = 60 m / (26 m/s * cos(34°))

Then, we can use the time to find the vertical distance using the formula d = v*t + (0.5)*g*t^2:

d = (26 m/s * sin(34°)) * t + (0.5) * (9.8 m/s^2) * t^2

Plugging in the values and solving the equation will give us the vertical distance between the fan and the gun when the t-shirt is caught.