The costumed mascot at a football game fires t-shirts from an air-driven t-shirt

Question

The costumed mascot at a football game fires t-shirts from an air-driven t-shirt gun with a muzzle speed of 15.0 m/s. The special limited edition shirts fly thorugh the air unaffected by air resistance and mustard stains, affected only by gravitational field of 9.80 m/s square.

part a) The maximum range occurs when the t-shirts gun launched at an angle of 45 degrees from the horizontal. What is the maximum range of the t-shirts gun if fired on ground level?

part b) If a t-shirts is fired stragiht upward from ground-level, how much time will the shirt be in the air before is strikes the ground?

part c) One of the t-shirts, fired at an angle 56.0 degree from the horizontal, knocks a hot dog from the hands of a seven years old fan, spilling mustard all over his clothes. If the shirt traveled a horizontal distance of 25 meters, how high above the t-shirts gun was the hot dog?

part d) If the t-shirts gun is launched at an angle of 75 degrees, what is the greatest height the shirt will reach? What horizontal distance will it travel in reaching its greatest height?

Explanation / Answer

Here

launch speed , u = 15 m/s

a) for maximum range ,

theta = 45 degree

maximum range = u^2 * sin(2 * theta)/g

maximum range = 15^2 * sin(90)/9.8

maximum range = 23 m

the maximum range is 23 m

b)

maximum height =u^2/(2 * g)

maximum height = 15^2/(2 * 9.8 )

maximum height = 11.5 m

c)

theta = 56 degree

x = 25 m

as the maximum range is 23 m

the tshirt will not reach 25 m away

part d)

greatest height = (v *sin(theta))^2/(2 * g)

greatest height = (15 * sin(75))^2/(2 * 9.8)

greatest height = 10.71 m

the greatest height is 10.71 m

horizontal distance = half range

horizontal distance = 0.5 * v^2 * sin(2 *theta)/g

horizontal distance = 0.5 * 15^2 * sin(150)/9.8

horizontal distance = 5.74 m

the horizontal distance at this point is 5.74 m

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