Question

At a football game, an air gun fires T-shirts into the crowd. The gun is fired at an angle of 46 degree from the horizontal with an initial speed of 27 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

Answer:

a) $t=3.199 seconds$

b) $h = 11.97 m$

Explanation:

Since this problem belongs to the concept of projectile motion

a) we know,

$Vcos\theta=\frac{R}{t}$

Where,

V = initial speed

Θ = angle with the horizontal

R = horizontal range

t = Time taken to cover the range 'R'

Given:

V = 27m/s

R = 60m

Θ = 46°

thus,

the equation becomes

$27\times cos46^o=\frac{60}{t}$

or

$t=\frac{60}{27\times cos46^o}$

$t=3.199 seconds$

b)The formula for height is given as:

$h = Vsin\theta \times t-\frac{1}{2}\times gt^2$

where,

g = acceleration due to gravity = 9.8m/s²

substituting the values in the above equation we get

$h = 27\times sin46^o\times 3.199-\frac{1}{2}\times 9.8\times 3.199^2$

or

$h = 62.124-50.14$

or

$h = 11.97 m$