Question

A conveyor belt at a recycling plant launches bottles and bottle caps into the air, so that an automatic image recognition device can count them. They land same height at which they are launched. Glass bottles are launched at an angle of 35.0 degrees above horizontal and land after 0.500 seconds.
a) Solve for the initial speed at which the bottles are launched.
b) Solve for the horizontal displacement at which the bottle land

Answer 1

(a) The initial speed at which the bottles are launched is 4.27 m/s.

(b) The horizontal displacement at which the bottle land is 1.75 m.

Initial speed of the bottle

The initial speed of the bottle is calculated as follows;

$T = \frac{2usin\theta}{g}$

where;

• T is time of flight
• u is the initial speed

2usinθ = Tg

u = Tg/(2sinθ)

u = (0.5 x 9.8)/(2 x sin35)

u = 4.27 m/s

Horizontal displacement of the bottle

X = u²sin(2θ)/g

X = (4.27² x sin(70))/(9.8)

X = 1.75 m

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