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NATURE.M

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## Homework Statement

You are at the mall on the top step of a down escalator when you lean over laterally to see your 1.80 m tall physics professor on the bottom step of the adjacent up escalator. Unfortunately, the ice cream you hold in your hand falls

out of its cone as you lean. The two escalators have identical angles of 40.0° with the horizontal, a vertical height of 10.0 m, and move at the same speed of 0.400 m/s. Will the ice cream land on your professor’s head? Explain. If it does land on his head, at what time and at what vertical height does that hap- pen? What is the relative speed of the ice cream with respect to the head at the time of impact?

## Homework Equations

Idea projectile motion:

Y=Y[itex]_{}(o)[/itex] + V[itex]_{}(yo)[/itex]t-1/2gt^2

X=X[itex]_{}(o)[/itex]+V[itex]_{}(x)[/itex]t

## The Attempt at a Solution

So for ice cream:

V[itex]_{}(xo)[/itex]=Vcosθ

V[itex]_{}(yo)[/itex]=-Vsinθ

Then,

Y[itex]_{}(ice cream)[/itex]= 10-Vsinθt-1/2gt^2

And for the professor:

Y[itex]_{}(prof)[/itex]=1.8+Vsinθ-1/2gt^2

Then equating Y[itex]_{}(ice cream)[/itex]=Y[itex]_{}(prof)[/itex], and solving for t,

I obtain t=15.946s. This value for time sees much to large. Any suggestions for what I may be doing wrong.